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AUTHOR: 


POLAND,  WILLIAM 


TITLE: 


RATIONAL  PHILOSOPHY 


PLACE: 


NEW  YORK 


DA  TE : 


1892 


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iJ  I    I  l.ui   jgmi  wn 


Poland,  William 

Rational  philosophy,  the  laws  of  thought 
formal  logic}  a  brief,  comprehensive  treati_. 
on  the  laws  and  methods  of  correct  thinking... 
New  York,  Silver,  1892. 

104  p.  diagrs.   19^  cm. 


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RATIONAL    PHILOSOPHY 


THE   LAWS  OF  THOUGHT 


OR 


FORMAL   LOGIC 

A  BRIEF,   COMPREHENSIVE   TREATISE   ON   THE 
LAWS   AND    METHODS   OF   CORRECT 

THINKING 


BY 


WILLIAM    POLAND 

Professor  of  Rational  Philosophy  in  St.  Louis  University 


SILVER,   BURDETT  &  CO.,   PUBLISHERS 
New  York         BOSTON  Chicago 

1892 


Copyright,  1892, 
By  silver,   BURDETT  &  CO. 


Typography  by  J.  S.  Gushing  &  Co.,  Boston. 


Presswork  by  Berwick  &  Smith,  Boston. 


Y 
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PREFACE. 


It  may  not  be  unwise  to  preface  the  following  pages 
with  a  caution  regarding  their  scope  and  purpose.  Such 
caution  may,  indeed,  be  due  not  only  to  the  writer  lest 
his  aim  be  misunderstood ;  but  also  to  the  reader,  who 
might  otherwise  seek  in  this  little  book  for  what  it  does 

not  contain. 

This  book,  then,  is  not  a  Psychology.  It  does  not 
discuss  the  nature  of  the  soul  or  of  its  faculties.  It 
merely  enumerates  the  principal  acts  of  the  intellect; 
and  describes  them  as  far  as  is  necessary  for  the  pur- 
pose of  this  book,  which  is  to  lay  down  briefly  and 
clearly  the  process  of  right  thinking.  This  requires  no 
encroachment  upon  the  field  of  psychology. 

Questions  which  should  be  discussed  later  on,  in  the 
course  of  philosophical  studies,  if  introduced  into  an 
outHne  of  correct  thinking,  only  retard  progress:  firstly, 
because  they  are  distracting;  but  especially  because 
the  mind  is  not  prepared  for  them.  Even  after  long 
discussions  they  are  not  understood  by  one  who  is  just 
entering  on  the  study  of  philosophy. 

Many  things  have  been    here  omitted    which  would 
find  a  fitting  place  in  an  exhaustive  treatise  on  Logic. 

3 


176816 


4  PREFACE. 

But  they  arc  such  things  as  arc  not  necessary  to  the 
purpose  of  this  compendious  work.  Just  as  there  are 
many  curious  combinations  of  numbers  which  might  be 
introduced,  and  sometimes  are  introduced,  into  an  arith- 
metic, but  which  are  of  no  essential  service  in  forming- 
an  accurate  and  rapid  accountant;  so  there  are  many 
things  —  curiosities  — which  may  be  introduced  into  a 
Logic,  but  which  are  in  nowise  necessary  to  prepare 
the  mind  for  accurate  and  ready  thought  in  the  study 
of  philosophy. 

On  the  other  hand,  this  book  is  not  intended  as  a 
sort  of  a  ''  Loo^ic  made  easy,''  or  **  Logic  in  tzcinfj'  hssotis 
without  a  waster^  In  philosophy  less  than  in  other 
things  can  we  ])rofitably  dispense  with  a  master. 

Finally,  attention  is  called  to  the  fact  that  terminology 
is  strictly  adhered  to,  both  for  the  sake  of  brevity,  and 
for  the  sake  of  the  learner's  progress,  that  he  may 
be  obliged  to  understand  each  .section  before  passing 
further. 


,\ 


'  1 

it 


CONTENTS. 


CHAPTER    I.     INTRODUCTORY. 

PAGE 

Article  I.     Logic. 

I.  Logic.     2.  Formal  and  Material  Logic.     3.  Natural  Logic. 

4.  Artificial  Logic.     5.  Logic  as  a  Science.     6.  As  an  Art    .       9 

Article  II.     Three  Acts  of  the  Mind. 

7.  Three  Acts.  8.  Knowledge  Representative.  9.  Simple 
Apprehension.  Idea.  10.  Judgment.  11.  Reasoning,  Argu- 
ment. 12.  Oral  Expression.  13.  Term.  14.  Proposition. 
15.  Syllogism u 


CHAPTER    II.     IDEAS  — TERMS. 

Article  I.    Ways  of  Classifying  our  Ideas. 

17.  Abstract,  Concrete.  18.  Clear,  Distinct,  Complete, 
Comprehensive.  19.  Singular,  Particular,  Collective,  Uni- 
versal      ic 

Article  II.     Classification  of  Universal  Ideas. 

20.  Form.  21.  Reflex  Universal.  22.  Species.  23.  Impor- 
tant Oi)servation.  24.  Genus.  25.  DiflTerence.  26.  Prop- 
erty.    27.  Accident.     28.  Heads  of  Predicables      .     .     . 


17 


Article  III.    Subordination  of  Genera. 

29.  The  Same  Form  Generic  and  Specific.     30.  Diagram. 

31.  Highest  Genus,  Lowest  Species,  Subaltern  Genera    .     . 

Article  IV.    Classification  and  Use  of  Terms. 

32.  Real  and  Logical  Terms.  33.  Univocal,  Equivocal, 
Analogous  Terms.  34.  Univocal.  35.  Equivocal.  36.  Anal- 
ogous.    37.  Supposition  or  Use ;  Material,  Logical,  Real     . 


22 


23 


r       ^r  ( 


()  CONTENTS. 

CHAPTER   III.     JUDGMENTS  AND   PROPOSITIONS. 

FAGE 

Article  I.    Definitions.    Structure  of  Propositions. 

38.  Ju(l<;ment.  39.  Proposition.  40.  Subject,  Copula, 
Predicate.     41.  Logical  and  (irammatical  Predicate    ...     27 

Article  II.    Simple  and  Compound  Propositions. 

42.  Simple.  43.  Compound.  44.  Variou.s  Constructions. 
41;.  Cateiiorical.  46.  Conditicmal.  47-  Conjunctive.  48-  Dis- 
junctive.     49-  Remark -^ 

Article  III.    Immediate  and  Mediate  Judgments. 

50.  All  Judgments.  51.  Immediate.  52.  Mediate.  53-  The 
Process    ^ 

Article  IV.    Connection  between  Subject  and  Predicate. 

54.  All  Judgments.  55.  A  Priori.  56.  A  Posteriori.  57.  No 
Synthetic  a  Priori 3^ 

Article  V.    Extension  and  Comprehension. 

58.  An  Axiom.  59.  Extension.  Txd.  Comprehension.  61.  Il- 
lustration      34 

Article  VI.  Extension  of  Propositions.  Quantity  and  Quality. 
62.  Extension.  63.  Tlie  Sul)ject.  64.  Note.  65.  The  Pred- 
icate. 66.  Universal  Affirmative.  67.  One  Exception. 
68.  Universal  Negative.  69.  Particuhu"  Affirmative.  70.  Par- 
ticular Negative.  71.  Two  Laws.  72.  Affirmative  and  Neg- 
ative.    73.  Negative  Particle.     74-  Quantity  and  Quality      .     36 

Article  VII.     Related  Propositions. 

75.  Three  Relationsliips.  76.  Conversion.  77.  Equiva- 
lence.    78.  Opposition.     79.  Diagram 4i 

CHAPTER    IV.      REASONING  — ARGUMENT. 

Article  I.     The  Syllogism. 

80.  Reasoning  and  Argument.  81.  Styles  of  Argument. 
82.  The   Syllogism.      83.  Antecedent,  Consequent,   Prem- 


CONTENTS. 


FAGS 


isses.  84.  Consequence.  85.  Axioms.  86.  Analysis  of 
Argument.     87.  Middle  and  Extremes 45 

Article  II.     Figures  and  Moods  of  the  Syllogism. 

88.  Major,  Minor,  Middle.  89.  First  Figure.  90.  Second 
Figure.     91.  Third  Figure.     92.  Moods  of  the  Syllogism     .     48 

Article  III.    Laws  of  the  Syllogism. 

93.  Scope  of  the  Laws.  94.  First  Law :  Three  Terms. 
95.  Second  Law:  Extension  of  Extremes.  96.  Third  Law: 
Extension  of  Middle  Term.  97.  Fourth  Law:  Place  of 
Middle  Term.  98.  Fifth  Law:  Affirmative  Conclusion. 
99.  Sixth  Law:  Negative  Conclusion.  100.  Seventh  Law: 
No  Conclusion.  loi.  Eighth  Law:  No  Conclusion. 
102.  Ninth  Law :  Particular  Conclusion.     103.  Caution        .     54 

Article  IV.    Some  Species  of  the  Syllogism. 

104.  Simple  and  Compound  Syllogisms.  105.  Conditional 
Syllogisms.  106.  Conjunctive  Syllogisms.  107.  Di.sjunc- 
tive  Syllogisms 61 

Article  V.     Other  Styles  of  Argument. 

108.  Argimient  Abbreviated.  109.  Enthymeme.  no.  Sori- 
tes.    III.  Polysyllogism.     112.  Epichirem.     113.  Dilemma    64 


CHAPTER   V.      TRUTH    OF  THE   PREMISSES. 

Article  I.    Formal  and  Material  Logic. 

114.  The  Form.  115.  The  Matter.  116.  Value  of  the 
Conclusion 68 

Article  II.    The  Demonstration. 

117.  Two  Kinds.  118.  Direct.  119.  Indirect.  120.  Sim- 
ple, Compound.     121.  A  Priori.     122.  A  Posteriori    ...     70 

Article  III.     Induction. 

123.  Deduction  and  Induction.  124.  Complete  Induction. 
125.  Incomplete  Induction.  126.  Example.  127.  Analogy. 
128.  Caution 73 


8 


CONTENTS. 


PAGE 


Article  IV.    Fallacies. 

129.  Fallacy.  130.  Petitio  Principii.  131.  Evadin«T  the 
(>c.stion.  132.  Of  the  Accident.  133.  A  Dicto  Simpliciter. 
134.  Of  the  Consequent.  135.  Of  the  Cause.  136.  Of  the 
(Question.     137.  Of  Reference.      138.  Of  Objections    .     .     .     jj 

CHAPTER   VI.      METHOD. 

Article  I.     Scientific  Method. 

139.  Scientitic  Method.     140.  Analysis  and  Synthesis      .     .     82 
Article  II.     Definition.  ^ 

141.  Definition.  142.  Nominal  Definition.  143.  Real  Defi- 
nition.     144.  Rules  for  Definition 83 

Article  III.     Division. 

145.  Scientific  Division.  146.  Physical  and  Metaphysical 
Parts.  147.  Actual  Union.  148.  Inte«;ral  Parts.  149.  Logi- 
cal Division.  150.  Potential  Parts.  151.  Logical  Whole. 
152.  Importance.     153.  How  to  Divide 87 

Article  IV.     Analysis  and  Synthesis. 

154.  The  Question.  155.  The  Answer:  Analysis,  Synthe- 
sis. 156.  Analysis.  157.  Synthesis.  158.  Exi)lanation 
Comi)lete.  159.  Singular  to  Universal,  and  vice  versa. 
160.  Complex  to  Simple,  and  vice  versa.  161.  Discovery 
and    Instruction.      162.  Analytic  and    Synthetic   Sciences. 

163.  Advice oi 

Article  V.    Science. 

164.  Science.  165.  Object  of  a  Science.  166.  Material  and 
Formal  Object.  167.  A  Delusion.  168.  Outline  of  the 
Sciences.     Explanation  of  Outline 96 

Points  for  Practice 100 

Inijex loi 


1 

ii 


\ 


'  I 


THE  LAWS  OF  THOUGHT. 


-0-0»<00- 


CHAPTER   I.      INTRODUCTORY. 


Article  I.     Logic. 

Logic  —  Formal  and  Material  Logic  —  Natural  and  Artificial  Logic. 

1.  The  name  Logic  comes  from  the  Greek,  X0709. 
A0709  signifies  reason,  thought;  also  oral  speech,  a  word. 
But  the  oral  word,  oral  speech,  is  merely  a  sign  of  what 
is  in  the  mind,  of  the  mental  word,  mental  speech, 
thought.      Logic,  therefore,  has  to  do  with  thought. 

2.  Formal  Logic  is  so  called  in  opposition  to  Material 
Logic,  because  it  deals  solely  with  the  form  or  structure 
of  thought,  of  an  argument;  and  not  with  the  matter 
contained  in  the  structure.  In  the  building  of  a  house 
there  are  different  persons  or  sets  of  persons  concerned. 
Besides  the  architect  there  are  those  who  supply  and 
prepare  the  material,  and  there  are  the  builders.  It  is 
the  business  of  the  architect  to  see  that  the  material 
is  supplied  and  properly  prepared  by  one  set  and  put 
together  by  the  other.  The  builders  have  not  to 
question  the  nature,  value  or  strength  of  the  material. 
They  have  only  to  see  that  the  pieces  fit.  They 
are  concerned  only  with  the  shape,  the  form  of  the 

9 


lO 


THE    LAWS    OF   THOUGHT. 


Structure  and  of  each  piece  as  tending  thereto.  Now, 
apply  this  to  the  edifice  of  knowledge.  Formal  logic 
has  to  do  with  the  principles  for  the  correct  putting 
together  of  the  material  furnished.  The  general  method 
of  furnishing  the  material  ready  prepared  is  the  sub- 
ject of  material  logic.  Hence  in  formal  logic  we  have 
to  work  at,  to  study,  only  the  correct >;7;/  of  thought; 
not  minding  whether  the  examples  we  take  to  practice 
upon  be  true  or  not:  just  as  one  wishing  to  illustrate 
the  structure  of  a  bridge  will  take  bits  of  wood,  paper, 
straw,  thread,  wire  or  whatever  he  may  find  at  hand] 
occupied  solely,  for  the  moment,  with  the  form ;  and 
not  at  all  concerned  about  the  material. 

3.  Natural  Logic.  Natural  logic  is  the  innate  dispo- 
sition all  men  have  to  think  correctly,  to  follow  certain 
rules  in  the  pursuit  of  knowledge,  of  truth.  We  are  all, 
by  nature,  logicians. 

4.  Artificial  Logic.  However,  as  sometimes,  even  with 
the  best  intentions,  we  are  liable  to  think  inaccurately 
by  reason  of  complications  of  notions  which  arise  and 
defects  which  are  easily  overlooked  in  the  process  of 
our  thought,  there  has  been  invented  what  is  called  an 
artificial  logic.  Not  that  there  is  anything  artificial  about 
it  in  the  sense  that  it  is  intended  to  replace  real  logic ; 
but,  in  this  sense,  that  it  is  made  an  art  whose  princi- 
ples we  can  learn  and  apply,  to  ensure  correct  thinking. 
The  methods  which  we  follow  when  we  think  correctly 
have  been  closely  observed  and  have  been  put  together 
as  a  connected  system  of  rules.  By  learning  to  apply 
them  we  can  acquire  the  art  of  logic. 

5.   Logic  as  a  Science.     But  logic  is  not  merely  an  art. 
It  is  primarily  a  science.     For  these  rules  are  a  system- 


INTRODUCTORY. 


II 


atized  body  of  fixed  laws  regarding  the  reason  of  cor- 
rectness in  thought.  Hence  logic  as  a  science  may  be 
defined :  '*  The  science  of  those  laws  which  must  rule 
the  acts  of  the  mind  in  correct  thinking." 

6.  Logic  as  an  Art.  Logic  becomes  an  art  when  these 
laws  are  presented,  or  made  ready  instruments,  for  use, 
to  ensure  right  thinking,  to  detect  false  reasoning,  and 
to  mend  faulty  argument. 


Article  II.     Three  Acts  of  the  Mind. 

Simple  Apprehension  ;  Judgment ;   Reasoning  —  Idea  ;  Judgment ; 
Argument  —  Term  ;  Proposition  ;  Syllogism. 

7.  Three  Acts  of  the  Mind.  To  find  out  the  rules  which 
we  must  follow  in  aiming  at  a  knowledge  of  truth,  we 
must  consider  three  acts  which  the  mind  performs  in 
obtaining  knowledge.  They  arc:  i.  Simple  Apprehen- 
sion;   2.  Judgment;    3.  Reasoning. 

8.  Knowledge  Representative.  All  knowledge  is  repre- 
sentative of  something  real  or  possible.  It  is  a  mental 
expression  of  that  something.  Hence  every  act  of  the 
mind  by  which  we  know  may  be  considered  in  two 
ways:  either  with  reference  to  the  degree  of  activity 
called  forth  or  with  reference  to  the  degree  in  which  it 
is  representative. 

9.  Simple  Apprehension.  Simple  apprehension  is  an 
act  by  which  the  mind  simply  perceives  or  apprehends 
something  without  aflFirming  or  denying  anything  about 
it.  If  we  consider  this  act  as  representative,  as  a  mental 
expression  of  that  something,  it  is  called  an  idea  (like- 


12 


THE    LAWS    OF    THOUGHT. 


INTRODUCTORY. 


13 


ness),  a  concept  (the  mind  conceiving  that  something  in 
itself,  in  likeness),  a  notion  (the  first  element  of  knowl- 
edge). Thus  by  the  act  of  simple  apprehension  we  may 
have  a  notion,  an  idea,  a  concept,  of  rose,  blue,  plant, 
cloth,  beauty,  justice,  etc. 

Remark  that  when  we  perceive  or  apprehend  we  do 
not  perceive  the  idea,  but  the  object  which  the  idea 
represents.  We  do  not  advert,  at  least  not  especially,  to 
the  act  of  the  mind.  It  is  only  by  a  second  act  of  the 
mind,   called   reflection,   that  we    perceive  we  are    per- 


ceivmg. 


10.  Judgment.  Judgment  is  that  act  by  which  the 
mind,  having  formed  two  ideas,  affirms  or  denies  identity 
between  their  objects.  Thus  :  The  rose  is  a  plant,  This 
cloth  is  not  blue.  Remark,  as  for  the  simple  apprehen- 
sion, that  what  we  affirm  or  deny  is  not  about  the  ideas, 
but  about  the  objects  which  the  ideas  represent.  This 
is  expressed  by  saying  that  we  affirm  or  deny  objective 
identity.  The  judgment,  as  the  simj)le  apprehension, 
may  be  regarded  as  a  certain  exercise  of  the  activity  of 
the  mind,  or  as  representative  of  the  presence  or  absence 
of  objective  identity.  As  an  act  it  is  called  judgment ; 
as  representative  it  is  also  called  a  judgment  or  a 
declaration. 

11.  Reasoning.  Reasoning  is  an  act  or  a  series  of  acts 
by  which  the  mind  compares  (objectively)  two  cases  pro- 
nounced upon  in  two  judgments,  and  in  that  compari- 
son perceiving  implied  the  material  for  a  third  judgment, 
thereupon  forms  explicitly  such  third  judgment  affirming 
or  denying  according  to  what  was  perceived  implicitly 
through  the  comparison.  This  definition  will  be  made 
sufficiently  clear  for  present  purposes  by  two  examples  : 


f; 


First  example.    The  judgment  makes  two  declarations : 


A  man  is  a  living  being; 
Hannibal  is  a  man. 


The  mind  compares  these  two  cases  and  then  declares 
explicitly  what  it  perceives  implied,  namely : 

Hannibal  is  a  lilting  being. 

Second  exainple.     The  judgment  makes  two  declara- 

I  J^f^^,f^^  /^  ^^  quadruped; 
This  feathered  being  is  not  a  quadruped. 

The  mind  compares  these  two  cases  and  then  declares 
explicitly  what  it  perceives  implied,  namely: 

This  feathered  being  is  not  a  horse. 

In  the  first  example  the  mind  worked  upon  the  prin- 
ciple that,  in  the  sense  in  which  two  things  {Jiving  being, 
Hannibal)  are  the  same  as  a  third  thing  {mati),  in  the 
same  sense  are  they  the  same  as  one  another.  In  the 
second  example  the  mind  worked  upon  the  principle  that, 
in  the  sense  in  which  two  things  {horse,  this  feathered 
being)  are,  the  one  (hoj'se)  the  same  as  a  third  thing 
{quadruped),  the  other  {this  feathered  being)  different 
from  it,  in  the  same  sense  are  they  different  from  one 
another. 

As  in  the  simple  apprehension  and  judgment  the 
action  of  the  mind  was  also  regarded  as  representative, 
so  the  act  of  reasoning  may  be  regarded  as  carrying  in 
its  third  judgment  a  new  representation  of  something 
perceived  through  the  two  prior  judgments.  Considered 
as  an  act  it  is  called  reasoning,  argumentation,  deduction. 
In  the  other  sense  it  is  called  argument,  and  also  some- 
times inference,  conclusion. 


14 


THE    LAWS    OF   THOUGHT. 


li 


12.  Oral  Expression  of  Thought.  Just  as  our  thoughts 
are,  as  it  were,  mental  words  expressing  certain  objects, 
so  in  written  and  spoken  words  do  we  express  our 
thoughts  as  well  as  the  objects  represented  in  our 
thought. 

13.  Term.  The  oral  {spoken )  or  written  word  express- 
ing an  idea  is  called  a  term,  as,  blue,  eloth,  justiee,  beauty. 

14.  Proposition.  The  terms,  oral  or  written  words, 
expressing  a  judgment  are  called  a  proposition,  as, 
Hanuibal  is  a  man. 

15.  Syllogism.  The  three  propositions  expressing  an 
argument  are  called  a  syllogism,  and  also  an  argument. 


1 


CHAPTER   II.     IDEAS,  TERMS. 

16.  We  shall  now  proceed,  within  the  limits  of  the 
scope  of  Formal  Logic,  to  make  some  considerations 
upon  ideas,  judgments,  arguments;  and  upon  their 
respective  verbal  expressions,  terms,  propositions,  syllo- 
gisms.    We  begin  with  the  most  elementary,  the  idea. 


Article  I.     Ways  of  Classifying  our  Ideas. 

Vh.    There   are   many   ways  of    partitioning   off   into 
classes  all  the  ideas  we  have  or  may  have. 

I.  Abstract  and  Concrete.  An  abstract  idea  is  one 
which  represents  its  object  as  independent  of,  taken 
asunder  from  {abstracted from),  everything  else.  A  con- 
crete idea  represents  its  object  as  coalescing  with,  in 
union  with,  grown  together  with  {concreted)  something 
else.  Our  ideas  of  bluettess,  wisdo^n,  are  abstract.  Our 
ideas  of  bltie,  wise,  are  concrete,  because  blue,  wise,  are 
thought  of  as  concreted  in  something  else  :  blue  sky,  wise 
Judge. 

18.  2.  Clear,  Distinct,  Complete  and  Adequate  or  Compre- 
hensive. According  to  the  degree  of  perfection  with 
which  ideas  express  the  characteristics  (called  tiotes)  of 
their  object,  they  are  divided  into  clear,  distinct,  complete 
and  adequate  or  comprcJicnsive. 

A  clear  idea  expresses  characteristics  or  notes  suf- 
ficient to  discern  the  object  from  others.     A  distinct 

«5 


i6 


THE    LAWS    OF    THOUGHT. 


IDEAS,    TERMS. 


17 


^ti 


idea  distinguishes  between  these  notes  themselves.  A 
complete  idea  expresses  all  the  notes  that  distinguish  the 
object  ///  reality  from  others.  A  comprehensive  or 
adequate  idea  expresses  all  that  can  be  perceived  in  the 
object:  the  human  intellect  has  no  such  idea  of  any- 
thing. 

I  see  an  object  moving  in  the  distance.  I  have 
an  indefinite,  obscure  idea  of  something  moving.  It 
approaches.  I  get  an  idea  of  my  friend  X  -  just 
enough  to  know  that  it  is  X  without  distinguishmg  any 
mark^  —  a  clear  idea.  X  comes  nearer.  Yes,  there  is 
the  walk  and  build  and  countenance  of  X.  My  idea  is 
becoming  distinct.  X  steps  up  and  shakes  hands  with 
me.  I  know  X  intimately  and  thoroughly.  I  note  all 
the  points  that  distinguish  him  as  X  from  aught  else. 
My  idea  is  complete. 

19.  3.  Singular,  Particular,  Collective,  Universal.  Ideas 
may  again  be  divided  according  to  the  number  of  indi- 
viduals embraced  in  the  idea  and  the  manner  of  embrac- 
ing them ;  that  is,  according  to  the  extension  of  the 
idea.  In  this  way  we  divide  ideas  into  singular,  par- 
ticular, collective,  universal. 

When  one  special  individual  is  expressed  in  a  deter- 
minate manner,  we  have  a  singular  idea.  Thus  :  Catuida, 
''  The  President,''  to-day,  this  book. 

When  the  idea  expresses  in  an  indeterminate  way 
some  one  or  other  individual  or  some  individuals,  it  is 
called  particular.  Thus  :  Some  man  or  other,  a  man,  a 
certain  man,  some  men. 

When  several  objects  are  expressed  under  one  idea 
or  concept,  but  in  such  a  way  that  the  idea  cannot  be 
applied  to  them  individually  but  only  as  a  collection,  the 


idea  is  called  collective.     Thus:  A  crowd,  a  fleet.     No 
individual  of  the  collection  is  a  crowd  or  a  fleet. 

When  several  objects  are  expressed  by  an  idea,  but  in 
such  a  way  that  the  idea  not  only  embraces  them  all, 
but  is  applied  to  them  distributively  and  individually, 
we  have  what  is  called  a  universal  idea.  Thus :  Man, 
horse,  gold.  I  can  say,  Man  is  a  living  being,  mean- 
ing that  all  men  are  living  beings ;  meaning  also  that 
each  individual  man  is  a  living  being.  When  I  say.  The 
horse  is  a  quadruped,  I  mean  that  all  are  quadrupeds, 
and  this  horse  is  a  quadruped.  When  I  say,  Gold  is  a 
metal,  I  mean  that  all  gold  and  that  this  piece  of  gold 

is  metal. 

This  partition  of  ideas  being  made,  we  have  to  deal 
now,  in  a  special  manner,  with  universal  ideas. 


Article  II.     Classification  of  Universal  Ideas. 

Species  —  Genus  —  Difference  —  Property  —  Accident. 
Heads  of  Predicables. 

20.  Form.  Universal  ideas  are  classified  according  to 
the  manner  in  which  the  one  idea  can  be  applied  to 
many  individuals ;  or,  what  comes  to  the  same,  accord- 
in"-  to  the  manner  in  which  what  the  idea  represents 
belongs  to  many  individuals.  This  will  explain  itself  as 
we  proceed.  Let  us  for  the  purpose  of  clearness  and 
brevity  introduce  a  new  word,  form  or  formality.  We 
shall  call  form  or  formality  whatever  can  be  the  object 
of  an  idea.  The  same  thing  may  have  m^ny  forms  (or 
determinations)  existing  in  it  simultaneously.  A  ball 
may  contain  the  forms  of   wood,  roundness,  whiteness. 


i8 


THE    LAWS    OF    THOUGHT. 


IDEAS,    TERMS. 


19 


elasticity,  etc.     In  man  there  are  the  forms  of  spirit, 
mattery  organisvi,  sensation,  etc. 

21.  Reflex  Universal.  Any  form  or  formality  may 
become  the  object  of  my  idea.  This  idea  I  may  reflect 
upon,  and  then  regard  as  applicable  not  only  to  the 
individual  form  from  which  I  first  got  it,  but  as  appli- 
cable to  an  indefinite  number  of  individual  cases,  actual 
or  possible,  and  also  as  sufficiently  representative  of  the 
same  formality  as  it  exists  or  may  exist  in  each  of  those 
cases.  I  begin  to  regard  the  idea  as  universal,  as 
applicable  to  many,  by  reflecting  upon  it.  The  idea,  as 
so  regarded  by  reflection,  is  called  a  reflex  universal  idea. 
Even  before  I  reflected  upon  it,  even  as  I  got  it  directly 
from  the  individual /6>;7;/,  it  was  in  itself  capable  of  being 
applied  to  the  indefinite  number  of  cases.  As  such, 
prior  to  reflection,  it  is  called  a  direct  universal 

22.  Species.  If  a  form  constitutes,  or  if  combined 
forms  constitute,  the  whole  essence  of  a  class  of  indi- 
viduals, so  that  no  individual  of  the  class  can  be,  or 
be  thought,  without  said  form  or  combination,  then  such 
form  or  combination  is  said  to  be  specific,  and  the  reflex 
universal  idea  representing  it  is  called  a  specific  idea. 
Thus  the  combination  of  rational  and  animal  in  man 
constitutes  his  essence.  The  complex  idea  I'ational 
animal  regarded  as  applicable  to  all  possible  men  is  a 
specific  idea. 

23.  Important  Observation.  Now  here  wc  have  some- 
thing curious  to  note.  The  idea  rational  animal  is  one 
idea  —  complex,  but  one.  Where,  when  we  apply  it  to 
all  men  actual  and  possible,  has  it  one  object }  When 
we  speak  of  the  i'ational  anifnal^  of  rational  animals,  of 


humanity,   we   find   ourselves   figuring   to   ourselves   a 
certain  something   outside  of    us  which  is  neither  this 
man  nor  that  man  nor  the  great  collection  of  all  men. 
Yet  is  it  something  which  we  do  put  up  before  us  as  the 
object    of    our   universal    reflex   idea,    rational  animal, 
humanity  ;  and  we  talk  of  it  as  if  it  were  something,  a 
man  in  general     We  know  that  what  we  say  of  it  is 
true  of  each  case  where  there  exists  the  rational  animal, 
where  there  exists  humanity.     What  is  it }     It  is  a  con- 
venience invented  by  the  ingenuity  of  the  mind  for  the 
needs  of    thought.     It  is  consequent  upon  the  innate 
tendency  of  the  mind  to  pursue  the  most  profitable  and 
expeditious   modes   of   thought.      It   is    something   we 
create   in   possessing  ourselves  of  the  reflex  universal 
idea.     It   is  a  something  that  does  service  for  all  the 
individual  cases.     We  call  it  the  species.     I  know  that 
the  expression  Junnan  species  suggests  to  us  the  whole 
collection  of  men,  and  that  naturalists  do  use  the  word 
species  to  express  collections.     But  we  do  not  reason  upon 
collections.     We  should  never  get  through.     Neither  do 
we  reason,  when  speaking,  for  instance,  of   man,  upon 
this  man  or  that  man.     When  we  say  man  is  mortal,  we 
speak  of  man,  in  general,  taken  as  a  species,  in  the  sense 
explained. 

24.  Genus.  If  the  form  be  something  that  is  found  in 
all  the  individuals  of  two  or  more  classes  so  as  to  con- 
stitute/^;-/ of  the  essence  of  such  individuals,  or  briefly, 
if  the  form  be  found  as  part  of  the  essence  in  two  or 
more  species,  it  is  called  generic,  and  the  reflex  universal 
idea  representing  it  is  called  a  generic  idea.  Thus  man 
and  brute  agree  in  this,  that  they  are  both  aiiimal ;  the 
formality  animal  is  of  the  essence  of  the  species  man 


i|WWHHI    '■Mil 


20 


THE    LAWS    OF    THOUGHT. 


and  of  the  species  bnitc.  Animal,  therefore,  is  generic^ 
and  applies  to  all  the  individuals  of  the  two  species.  If 
now  we  j)ut  before  us  that  certain  somethinp^  which  will 
stand  as  one  for  all  the  individuals  possessing  animal 
nature,  we  shall  have  what  is  called  a  genus. 

25.  Difference.  Now  take  two  species.  They  agree 
in  something  that  is  common  to  the  essences  of  both. 
This,  as  we  have  said,  is  genus.  But  they  differ  also  in 
other  essentials.  All  the  individuals  of  one  species  have 
a  formality  which  is  not  in  any  of  the  individuals  of  the 
other,  and  which  distinguishes  all  the  individuals  of  one 
from  all  those  of  the  other.  The  reflex  universal  idea 
of  this  formality  is  called  a  differential  idea  ;  and  as  this 
stands  out  objectively  in  the  species,  it  is  called  a  differ- 
ence or  specific  difference.  Take  the  genus  anivial.  It 
embraces  the  two  species,  rational  animal  and  irrational 
animal.     Rational  and  irrational  are  specific  differences. 

26.  Property  or  Inseparable  Accident.  Sometimes 
there  is  found  a  form  in  all  the  individuals  of  a  species, 
which  form,  though  not  of  their  essence,  is  still  neces- 
sarily connected  with  the  essence  and  flows  from  it. 
The  reflex  universal  idea  of  a  form  so  considered  is  said 
to  be  the  idea  of  a  property.  Such  form,  considered  in 
the  species,  as  we  have  explained  species,  is  named  a 
property  or  an  inseparable  accident.  Such  may  be  con- 
sidered, for  instance,  the  powers  of  speech  and  of 
laughter  in  man. 

27.  Accident.  If,  however,  a  certain  form  happen  to 
be  common  to  many  individuals,  but  be  in  nowise  of 
their  essence  nor  necessarily  connected  therewith,  and 
be  such  that  it  can  be  added  or  taken  away  without 


IDEAS,    TERMS. 


21 


affecting  the  essence,  such  form  is  said  to  be  simply 
accidental.  The  universal  reflex  idea  representing  it  as 
so  separable  is  the  idea  of  an  accident.  The  form  itself, 
in  whatever  way  considered,  as  thus  separable,  is  called 
an  accident.  Thus  the  forms,  blue,  green,  circular,  square, 
tJiick,  soft,  etc.,  are  separable  accidents.  We  distinguish 
the  inseparable  accidents  by  the  special  name  of 
property. 

28.  Heads  of  Predicables.  The  wide  reaching  nature 
of  the  classification  which  has  just  been  given,  will  be 
seen  if  we  consider  that  whatever  we  affirm  or  deny  of 
anything  is  affirmed  or  denied  as  a  gcfius,  species,  differ- 
ence, property  or  accident.  That  is  to  say,  whatever 
we  predicate  (affirmatively  or  negatively)  we  predicate 
(affirmatively  or  negatively)  as  the  genus,  species,  etc.,  of 
that  of  which  we  predicate  it.  Thus  we  say  fna^i  is  a 
rational  animal.  We  predicate  rational  animal  of  man. 
We  predicate  it  as  the  species.  If  we  say  7nan  is  ratiojial, 
we  predicate  rational  as  the  specific  difference.  If  we 
say  man  is  an  a?iimal,  we  predicate  animal  as  the  genus. 
If  we  say  the  man  is  luhite,  yellow,  strong,  we  predicate 
ivliite,yelloiv,  strong  as  accidental,  as  accidents.  Hence 
genus,  species,  differoice,  property,  accident,  are  called 
Heads  of  predicables,  because  whatever  is  predicable  of 
anything  comes  under  one  of  these  heads.  There  is  a 
single  exception  to  this  general  law.  The  exception  is 
for  the  form  being.  Being  applies  to  whatever  can 
exist  or  be  thought  of.  The  idea  of  being  is  said  to  be 
transcendental.  But  the  predication  of  being  (as  also  of 
one,  true,  good)  constitutes  one  of  the  most  subtle  dis- 
cussions of  general  metaphysics.  We  need  not  speak 
of  it  here. 


22  THE    LAWS    OF    THOUGHT. 


Article  III.     Subordination  of  Genera. 

Highest  Genus  —  Subaltern  Genera  —  Lowest  Species  —  Individuals. 

29.  The  Same  Form  Generic  and  Specific.  It  is  to  be 
remarked  that  there  are  cases  where  the  same  form 
considered  as  a  universal  is  capable  of  beini;  regarded 
as  both  gcfius  and  species.  Take,  for  instance,  the  form 
substance.  Since  the  individuals  to  which  it  extends 
can  be  divided  into  the  two  classes,  corporeal  substance 
(body)  and  incorporeal  substance  (spirit),  it  is  jrenus  with 
reference  to  them,  and  they  are  species  embraced  by  it. 
lUit  the  form  corporeal  substance  (body)  is  again  a  genus 
when  regarded  as  universal,  for  it  extends  to  individuals 
that  can  again  be  divided  into  classes,  —  organic  body  and 
inorganic  body.  These  become  species  under  it.  Or- 
ganic body,  next  taken  as  a  universal,  becomes  a  genus 
with  reference  to  the  classes  sentient  organic  body  (ani- 
mal) and  non-sentient  organic  body  (plant).  These  are 
species  under  it.  But  a}iimal  is  also  genus  with  refer- 
ence to  rational  animal  and  irrational  animal. 

30.  Diagram.     The  following  plan  will  exhibit  this  to 
the  eye : 

Substance. 


IDEAS,  TERMS. 


23 


Corporeal  Substance  or  Body.         Incorporeal  Substance. 


Organic  Body. 


Inorganic  Body 


Sentient  Organic  Body  or  Animal.  Non-sentient. 


Rational  Animal  or  Man. 


Irrational. 


Charles,  Frederic,  Augustus,  etc.  | 


31.  Highest  Genus,  Lowest  Species,  Subaltern  Genera. 
In  this  table  it  is  seen  that  substance  is  used  as  ge7ius 
only.  Body,  organic  body  and  animal  are  used  both 
as  species  and  as  genus.     Man  is  used  as  species  only. 

When  a  genus  cannot  be  considered  as  a  species 
under  a  higher  genus,  it  is  called  highest  genus. 

When  a  species  under  one  genus  cannot  be  made  a 
genus  with  reference  to  individuals  under  it,  that  is, 
when  the  individuals  cannot  be  classified  as  species,  it  is 
called  lowest  species. 

The  forms  that  are  predicable  both  as  genus  and  as 
species  are  called  subaltern  genera. 

In  the  table.  Substance  (supposing  it  to  be  incapable 
of  being  ranged  as  species  under  a  higher  genus)  is 
highest  genus.  Man  is  lowest  species.  Body,  Organic 
Body,  Animal,  are  subaltern  genera.  Charles,  Frederick y 
Augustus,  etc.,  are  merely  individuals  of  the  species 
man. 


Article  IV.     Classification  and  Use  of  Terms. 

Real,  Logical  —  Univocal,  Equivocal,  Analogous  —  Supposition. 

32.  Real  and  Logical  Terms.  We  may  now  say  a  word 
about  tenns.  Terms  are  the  written  or  spoken  words 
that  stand  for  ideas  or  for  the  objects  of  ideas.  A  term 
is  called  real  when  it  expresses  an  object  as  that  object 
may  exist  independently  of  the  mind.  Thus  London, 
this  man,  are  real  terms.  A  term  is  called  logical  when 
it  expresses  an  object  in  that  kind  of  existence  which 
depends  entirely  on  the  mind,  as  man,  animal,  used  in 
the  universal  sense  to  stand  for  genus  or  species,  v.  gr., 
for  animal  and  man  in  general.    Genus  and  species  as  we 


24  THE    LAWS    OF    THOUCIHT. 

have  explained  them  are  mental  ereations,  doing  service 
as  representatives  for  a  class,  or  what  is  the  same,  their 
existence  is  logical,  dependent  on  the  mind.  Hence  the 
terms  expressing  them  as  such  are  called  logical  terms. 

33.  Univocal,  Equivocal,  Analogous  Terms.  Leaving 
the  real  terms  and  concerning  ourselves  solely  with  the 
logical,  we  find  that,  on  account  of  the  defects  of 
language,  some  terms,  doing  service  as  universals,  do 
not  always  represent  the  same  ideas  nor  apply  in  the 
same  manner  to  all  the  individuals  for  which  we  make 
them  stand.  We  find  terms  to  be  not  only  univocal ^ 
but  also  equivocal  and  analogous. 

34.  Univocal.  That  term  is  called  univocal  (one  word) 
which  is  really  but  one  term  in  meaning  as  well  as  in 
sound.  That  is  to  say,  the  univocal  term  is  always 
applied  with  the  same  signification  to  each  and  all  of 
the  inferiors  {i.e.  species  or  individuals)  to  which  it  can 
be  applied.     Such  are  the  terms,  animal,  man. 

35.  Equivocal.  But  if  the  same  written  or  spoken 
word,  the  same  term,  comes,  in  the  complexity  of 
language-growth,  to  stand  for  two  or  more  different 
ideas  and  objects  of  ideas,  it  is  called  an  equivocal  term. 
Thus  the  term  pen  is  equivocal.  It  is  a  ivord  that 
serves  equally  to  express  different  ideas  and  objects  of 
ideas.  It  stands  equally  for  a  zu riling  instrumoit  and  a 
cattle  enclosure.  The  equivocation  is  sometimes  in  the 
sound  only,  as  bow  (a  reverence)  and  bough.  Sometimes 
it  is  in  the  writing  only,  as  bow  (a  reverence)  and  boiu  (in 
archery). 

36.  Analogous.  Again,  there  are  terms  that  are  ap- 
plied to  different  things  neither  univocally  {i.e.  in  quite 


IDEAS,  TERMS. 


25 


the  same  meaning),  nor  equivocally  {i.e.  in  quite  different 
meanings),  strictly  speaking.  The  same  term  is  used 
on  account  of  some  connection  between  the  objects. 
The  connection  is  called,  in  philosophy,  analogy.  The 
terms  are  called  analogous  terms. 

When  the  atuilogy  or  connection  is  merely  a  likeness 
between  the  objects,  it  is  called  analogy  of  proportion. 
We  make  this  the  ground  for  the  use  of  the  metaphor. 
We  will  call  a  man  a  lion  on  account  of  his  courage. 
We  merely  abbreviate  a  comparison. 

There  is  another  analogy  where  the  connection  is 
closer.  We  say  a  healthy  man  and  also  (however  justly) 
a  healthy  climatCy  a  healthy  complexion.  We  affirm  of 
the  climate  (which  is  the  cause)  and  of  the  complexion 
(which  is  a  natural  sign)  the  attribute  which,  in  its  full, 
original  and  proper  meaning,  belongs  only  to  the  man. 
We  have  here  again,  strictly  speaking,  figures  of  speech. 
This  analogy  is  closer  than  the  mere  similitude.  It  is 
called  analogy  of  attribution.  However,  it  is  specified  as 
analogy  of  extrinsic  attribution,  because  the  form  that 
is  attributed,  health,  is  intrinsic  to  man  only,  belongs  to 
man  only,  and  is  extrinsic  to  climate  and  to  complexioty 
they  being  but  the  cause  and  the  sign  of  man's  health. 
But  we  have  introduced  this  question  only  to  come  to 
what  is  called  the  analogy  of  intrinsic  attribution.  And 
we  speak  of  the  analogy  of  intrinsic  attribution  only  as 
an  aid  to  the  understanding  of  a  later  question,  the 
subtle  question  of  the  attribution  of  being,  referred  to 
in  28.     Therefore  — 

What  is  attributed  may  really  exist  in  all  the  individu- 
als to  which  it  is  attributed,  and  still  not  in  such  a  way 
that  it  can  be  attributed  ujiivocally,  i.e.  in  the  very 
same  sense  and  manner.     It  exists  in  one  independently 


26 


THE    LAWS    OF   THOUGHT. 


of  all  the  others,  but  in  the  others  only  dependently 
upon  this  one.  Thus  being  is  predicated  of  God  and 
of  created  tJii)igs :  of  God,  independently;  of  created 
things,  only  with  dependence  upon  the  Creator.  Being 
is  not  used  nnivoeally.  It  does  not  apply  in  the  same 
sense  to  Creator  and  Creation.  It  cannot  be  called 
genns.  Under  genus  the  species  are  independent  one 
of  another.  But  this  question  will  be  treated  in  the 
General  Metaphysics. 

37.  Supposition.  The  snpposition  of  a  term  is  what  is 
siib-posed  by  {put  under)  the  term,  what  is  implied  by  it 
or  intended  to  be  understood  by  it.  This  depends  upon 
the  wish  of  the  one  who  uses  the  term.  We  might 
extend  this  subject  and  go  back  over  all  the  various 
classifications  of  ideas  and  their  corresponding  objects. 
We  shall  give  but  three  wide  divisions  of  the  supposi- 
tion and  thus  close  this  chapter. 

The  supposition  is  said  to  be  material  when  we  imply 
no  more  than  is  evident  from  the  7nere  sound  of  the 
term  or  its  appearance  as  written.  Thus,  when  we  say 
or  write,  Man  is  a  word  of  one  syllable ^  our  use  or  sup- 
position of  the  term  man  is  material. 

If  we  imply  that  the  term  is  used  in  the  universal 
sense  to  stand  for  genus  or  species,  the  supposition  is 
called  logical.  In  the  sentence,  Man  is  a  rational  ani- 
mal, the  supposition  of  the  term  ma)i  is  logical. 

When  we  wish  the  term  to  stand  for  a  reality,  the 
supposition  is  called  real.  In  the  sentence,  This  man 
is  temperate,  the  supposition  of  the  term  man  is  real. 


CHAPTER  III.     JUDGMENTS,  PROPOSITIONS. 


Article  I.     Definition  and  Structure  of 

Propositions. 

38.  Judgment.  'Y\i(t  judgment,  as  we  have  said,  is  that 
act  of  the  mind  by  which  we  compare  two  objects  of 
thought  and  pronounce  upon  their  identity  or  agree- 
ment, affirming  or  denying.  It  is  an  affirmation  or  a 
denial. 

It  is  not  always  necessary  that  any  appreciable  time 
should  be  taken  to  compare  the  terms  before  passing 
sentence.  There  may  be  and  there  are  cases  where 
the  verdict  is  evident  at  once  upon  the  presentation  of 
the  terms.  We  see  at  once  the  identity  or  the  disagree- 
ment. Our  daily  thoughts  are  full  of  instances  in 
point. 

39.  Proposition.  We  have  already  stated  that  the 
judgment  as  expressed  in  spoken  or  written  words  is 
called  2l  propositiott. 

40.  Subject,  Copula,  Predicate.  A  proposition  consists 
of  three  parts,  subject,  copula,  predicate.  The  subject  is 
that  of  which  something  is  affirmed  or  denied.  The 
predicate  is  that  which  is  affirmed  or  denied  of  the  sub- 
ject. The  copula  is  a  word  or  words  expressive  of  the 
affirmation  or  denial,  the  words,  namely,  is,  are,  is  not, 
are  not. 

27 


28 


THE    LAWS    OF   THOUGHT. 


PREDICATE. 

rational, 
virtue, 
detestable, 
saints. 


JUDGMENTS,    PROPOSITIONS. 


29 


SUBJECT. 

COPULA. 

Man 

is 

Knowledge 

is  not 

Vices 

are 

Sinners 

are  not    , 

The  copula  is  a  convenience  of  language.  It  merely 
stands  for  the  agreement  or  disagreement  that  exists  in 
the  objects  ;  this  agreement  or  disagreement  is  perceived 
by  the  mind  comparing  the  ideas,  and  is  finally  pro- 
nounced upon  in  the  judgment. 

41.  Logical  and  Grammatical  Predicate.  We  must  be 
careful  to  distinguish  between  the  predicate  of  the 
loi^ician  and  the  predicate  of  the  o;yammarian.  In  the 
sentence,  Birds  fly,  the  grammarian  may  tell  us  that/j' 
is  the  predicate.  The  logician  will  resolve  the  sentence 
in  such  a  way  as  to  employ  the  copula.  He  will  say. 
Birds  are  heings-thatfly ;  and  with  him  the  predicate  is 
beings-thatfly.  Thus  the  logician  will  transform  any 
sentence  to  put  it  into  logical  shape. 


Article  II.     Simple  and  Compound  Propositions. 

Simple  -  Compound  -  Copulative  -  Disjunctive  -  Conditional  — 

Causal. 

42.  A  Simple  Proposition  contains  but  one  principal 
subject  and  one  principal  predicate.  The  ship  is  sailing, 
is  a  simple  proposition.  We  may  add  circumstances  of 
time  and  place,  adjectives,  adverbial  and  relative  clauses, 
without  making  it  a  compound  proposition.  It  will 
become  complex,  but  not  compound.      The  ship  that  was 


i 


made  last  year  at  Nezu  York  is  sailing  amid  icebergs  that 
have  floated  from  Greenland  to  the  coast  of  Newfoundland, 
is  still  for  the  logician  a  simple  sentence  though  complex. 
All  that  belongs  to  ship  goes  in  as  subject.  All  that 
belongs  to  sailing  goes  in  as  predicate. 

43.  A  Compound  Proposition  contains  two  or  more 
principal  subjects  and  predicates  expressed  or  implied. 
Paris  and  Berlin  are  beautiful  is  a  compound  proposi- 
tion and  stands  for  the  two  simple  propositions  Paris  is 
beautiful,  Berlin  is  beautiful  Add  another  predicate : 
Paris  and  Berlin  are  large  and  beautiful.  Here  we 
have  four  simple  propositions  in  the  compound. 

44.  Various  Constructions.  There  arc  various  kinds 
of  simple  and  compound  propositions  —  various  as  the 
grammatical  constructions  invented  to  secure  brevity  in 
language,  the  sometimes  cumbersome  vehicle  of  thought. 
The  propositions  receive  their  names  from  the  construc- 
tions.    We  call  attention  to  a  few  propositions. 

45.  Categorical.  A  categorical  proposition  is  one  that 
affirms  or  denies  absolutely  and  directly.  It  may  be 
simple  or  compound.  Thus :  Man  is  rational.  The  soul 
is  not  material,  Prudence  and  Justice  are  virtues,  Camels 
and  giraffes  are  not  insects. 

46.  Conditional.  A  conditional  proposition  affirms  or 
denies  not  absolutely,  but  on  condition.  The  rain  is 
coming  is  categorical.  But,  If  the  wind  is  west,  the  rain 
is  coming  is  a  conditional  proposition.  Remark  that 
this  is  really  a  simple  proposition.  We  do  not  say.  The 
ivind  is  west,  the  rain  is  coming.  We  merely  affirm  con- 
ditional connection  between  the  two.  The  conditional 
proposition  is  also  called  hypothetical. 


30 


THE    LAWS    OF    THOUGHT. 


47.   Conjunctive.     A  conjunctive   proposition    affirms 
the   simultaneous    incompatibility   between   two   cases. 
No  man  can  spend  all  his  money  on  drink  and  still  sup- 
port his  family.     Here  we  do  not  affirm   or   deny  the 
categorical    propositions  that  he   spends   his   money  on 
drink,  that  he  supports  his  family.     We  affirm  only  the 
incompatibility  between   the   two.     The   proposition  is 
simple,  however  complicated  in  language.     The  conjunc- 
tive proposition  is  reducible  to  the  conditional  thus :  If  a 
man  spends  all  his  money  on  drink,  he  cannot  support  his 
family.      The    conjunctive    proposition   is   therefore   a 
species  of  the  hypothetical.     It  is  always  negative.     It 
is  called  conjunctive  for  the  sake  of  a  name,  on  account 
of    the   conjunctive   particle   and  which   connects   the 
incompatible  cases. 

48.  Disjunctive.  A  disjunctive  proposition  is  made 
up  of  two  or  more  categorical  propositions  connected 
in  such  way  by  a  disjunctive  particle  that  no  one  is 
declared  absolutely,  but  the  acceptance  of  one  implies 
the  rejection  of  the  others.  Thus,  speaking  of  a  per- 
son's age,  I  may  say,  He  is  either  just  fifty  or  under 
fifty  or  past  fifty.  Suppose  I  declare  categorically  that 
he  is  just  fifty ;  then  the  two  other  parts  become  he  is 
not  under  fifty,  he  is  not  past  fifty.  However,  the  denial 
of  one  case  does  not  imply  the  affirmation  of  the  other 
two.  If  I  say,  He  is  not  just  fifty,  I  may  not  therefore 
affirm  both  that  he  is  under  fifty  and  that  he  is  past 
fifty.  The  remaining  parts  are  simply  left  in  the 
diminished  disjunctive  proposition,  He  is  either  under 
fifty  or  past  fifty.  The  disjunctive  proposition  is  a 
species  of  the  hypothetical,  with  one  part  positive  and 
the  other  part  negative.     Thus :  If  he  is  just  fifty,  he  is 


JUDGMENTS,   PROPOSITIONS. 


31 


neither  under  fifty  nor  past  fifty.  As  the  example  given 
implies  two  such  conditions,  we  might  class  it  with  the 
compound  propositions ;  but  this  matters  nothing  to  our 
purpose. 

49.  Remark.  Here  we  shall  leave  the  complex  and 
compound  propositions.  We  have  mentioned  the  con- 
ditional, conjunctive  and  disjunctive,  because  we  shall 
have  occasion  to  refer  to  them  when  treating  of  the 
varieties  of  the  syllogism. 

Henceforth  in  the  present  chapter  we  shall  confine 
our  study  to  the  elementary  proposition,  the  simple  cate- 
gorical proposition. 


Article   III.     Immediate  and  Mediate  Judgments. 

50.  All  Judgments.  The  judgments  we  form  are  all 
necessarily  either  immediate  or  mediate. 

51.  Immediate.  An  immediate  judgment  is  one  that 
is  formed  without  a  process  of  reasoning.  If  some  one 
says  to  me,  A  zvhole  orange  is  greater  than  half  an  orange, 
I  do  not  ask  him  to  prove  it.  I  see  the  truth  immedi- 
ately, and  pronounce  upon  i:  without  having  to  be  led 
to  see  it  through  the  medium  of  other  truths  better 
known.  Again,  if  I  take  a  piece  of  heated  iron  in  my 
hand,  I  can  and  do  know  and  say  at  once,  This  iron  is 
hot.  '  I  do  not  have  to  go  through  any  other  judgment 
to  arrive  at  the  knowledge  that  this  iron  is  hot.  The 
judgment  is  immediate. 

52.  Mediate.  On  the  other  hand,  if  some  one  tells  me 
that  the  three  angles  of  a  triangle  are  equal  to  two  right 
angles,  I  do  not  see  at  once  that  it  is  so ;  I  ask  him  to 


32 


THE    LAWS    OF    THOUGHT. 


show  me  that  it  is  so.     And  he  proceeds  to  put  before 

me  other  propositions  through  which  I  see,  until  it  dawns 

upon  me  that  what  he  said  at  first  is  true.     These  other 

propositions  or  truths  are  the  incdiinn  through  which  I 

see  that  the  three  unifies  are  equal  to  two  riisht  a;i<r/cs. 

This  judgment  is  therefore  called  a  mediate  judgment. 

To  take  another  example.     I  hand  a  banknote  to  some 

one,  as  payment.      He  tells  me,  T/tis  banknote  is  a  eoun- 

terfeit.     I  do  not  perceive  that  the  note  is  a  counferfeit. 

He  imparts  to  me  some  new  knowledge,  and  through  the 

viedium  of  that  knowledge,  I  too  can  see  and  say.  This 

note  is  a  eounterfeit.     My  judgment  is  mediate. 

53.  The  Process.  The  process  by  which  one  judgment, 
proposition,  is  made  evident  through  the  medium  of 
others  is  called  reasoning.  This  will  form  the  subject 
of  the  next  chapter.  We  have  still  to  consider,  in  this 
chapter,  two  other  divisions  of  judgments  or  propositions. 
This  we  shall  do  in  the  two  following  articles. 


Article  IV.     Connection  between  Subject  and 

Predicate. 

A  Priori,  A  Posteriori  —  Necessary,  Contingent  —  Absolute,  Hypo- 
thetical—Metaphysical, Physical  — Analytical,  Synthetical. 

54.  All  Judgments.  If  we  consider  the  connection 
that  exists  between  the  predicate  and  the  subject,  we 
can  classify  all  judgments  as  a  priori  or  a  posteriori. 

55.  A  Priori.  If  the  predicate  is  such  that  it  is  always 
implied  in  the  subject,  and  in  such  way  that  a  full  under- 
standing of  what  is  meant  by  the  subject  and  predicate 
is  sufficient,  without  any  experiment  upon  a  particular 


judgments,  propositions. 


33 


f 


If 


case,  to  make  us  see  that  the  proposition  holds  in  all 
cases,  absolutely,  necessarily  and  without  possible  excep- 
tion, the  proposition  or  judgment  is  called  a  priori.  It  is 
seen  to  hold  prior  to  any  application  to  a  particular  case. 
A  ivhole  is  greater  than  any  of  its  parts  ;  no  thing  ean 
simultaneously  exist  and  not  exists  —  these  are  a  priori 
propositions. 

Such  propositions  are  also  called  7iecessary,  because 
an  exception  is  impossible.  They  are  called  absolute, 
because  they  hold,  absolved  from,  free  from,  all  condi- 
tion. They  are  called  metaphysical,  because  their  truth 
does  not  depend  upon  the  physical,  actual  order  of 
things  existing.  They  are  called  analytical,  because  by 
analyzing  the  subject,  by  taking  it  asunder  into  all  that 
it  implies,  we  will  finally  arrive  at  the  predicate  and  see 
that  the  predicate  belongs  to  the  subject. 

56.  A  Posteriori.  An  a  posteriori  proposition  is  one 
in  which  the  idea  of  the  predicate  is  not  implied  in  the 
idea  of  the  subject.  Some  one  says  to  me.  This  iron  is 
hot.  I  may  know  all  that  books  can  teach  about  the 
nature  of  iron  and  the  nature  of  heat.  But  all  of  it  will 
not  teach  me  that  this  iron  is  hot.  I  must  have  experi- 
ence of  this  particular  case  of  iron  and  heat.  After  the 
test,  posterior  to  the  experience,  I  may  affirm.  This  iron 
is  hot.     Hence  the  name  rt'/^J'/rr/^r/. 

Such  propositions  are  also  called  co7itijigent,  as  opposed 
to  necessary,  because  they  may  happen  to  be  true  or  not 
true.  They  are  called  hypothetical,  as  opposed  to  abso- 
lute, because  their  truth  depends  upon  a  supposition,  a 
hypothesis,  which  may  be  wanting.  They  are  called 
physical,  because  they  represent  facts  of  the  actual, 
physical    order.     Finally,  they  are   called   syiithetic,  as 


34 


THE    LAWS    OF    THOUGHT. 


opposed  to  analytic,  because  they  are  made  up  by  the 
synthesis,  the  putting  together,  of  two  ideas,  terms, 
neither  of  which  is  found  in  the  analysis  of  the  other. 

57.    Synthetic  a  Priori.     We  have  here  to  make  a  re- 
mark upon  an  assertion  of  Emmanuel  Kant  which  has 
caused  a  great  deal  of    confusion  in    philosophy.      He 
asserted  that  there  could  be  a  proposition  which  would 
be  at  once  synthetic  and  a  priori,  and  he  called  it  the 
synthetic  a  priori.     Kant   illustrates  his  discovery  with 
examples.     For  instance,   he    draws   upon  arithmetical 
addition.      The     proj)()siti()n     three    and  tzco   are  Jive, 
3  -h  2  =  5,  is  with  him  synthetic  a  priori :  a  priori,  because 
it  is  absolute ;  synthetic,  because,  he  says,  the  i)redicate 
five,  5,  adds  on  a  new  notion  over  and  above  three  and 
two,  3  +  2.     Let  us  see  if  the  predicate  adds  a  new  idea. 
We  repeat  what  we  said  before,  that  we  do  not  reason 
with  the  mere  sound  of  the  voice  or  the  mere  a])j)ear- 
ance  of  marks  on  paper.     What  does  the  subject  mean  > 
3  means  i  +  i  -f  i.      2  means   i  +  i.      34-2  means  i  + 
I  H-  I  +  I  -f  I.      5    means    i  +  i  -|- 1  -f  i  -f-  i.      Now   put 
down  the  meaning  of  3  +  2  =  5,  and  you  have  i  +  i  +  i 
-M-fi  =  i-hi  +  i-fi-hi.      What    is    there    in    the 
predicate  that  is  not  in  the  subject.'* 


Article  V.     Extension  and  Comprehension. 

58.  An  Axiom.  We  have  delayed  to  this  point  a  very 
important  consideration  on  the  subject  of  ideas  and  terms. 
We  have  delayed  it  on  account  of  its  immediate  use  in 
the  next  article.  In  fact,  we  do  not  hesitate  to  say  that 
the  thorough  understanding  of  the  subject  of  the  present 


judgments,  propositions. 


35 


'i 


article  is  the  key  to  philosophy.  There  is  an  old  axiom 
in  philosophy  which  runs  thus :  TJie  greater  the  extension, 
the  smaller  the  comprehension  ;  or  TJie  smaller  the  com- 
prehension, the  greater  the  extension  ;  or  Widen  the  exten- 
sion, and  you  diminish  the  compreJiension  ;  or  Expand  the 
comprehension,  and  you  narrow  the  extcjision.  All  mean 
the  same  thing.     But  what  do  they  mean } 

59.  Extension.  The  extension  of  an  idea  or  a  term 
refers  to  the  number  of  individuals  to  which  it  can  apply. 

60.  Comprehension.  The  comprehension  of  an  idea 
or  of  a  term  refers  to  the  number  of  ideas  or  terms  im- 
plied in  said  idea  or  term. 

61.  Illustration.  Take  the  idea,  animal.  It  can  apply 
to  —  that  is,  it  extends  to  all  individuals  in  which 
there  is  animal  nature.  But  combine  it  with  the  idea 
rational,  so  as  to  have  rational  animal,  or  man.  At 
once  you  shut  out  from  its  application  all  irrational 
animals.  You  cut  them  off  from  its  extension.  You 
narrow  its  extension.  Why.?  Because  you  have  ex- 
panded the  comprehension.  The  idea  man  comprehends 
not  merely  animal  but  animal  +  rational.  If  you  expand 
the  comprehension  by  adding  the  term  ivhite,  so  as  to 
have  white  man,  you  will  diminish  the  extension  by 
cutting  off  all  men  who  are  not  white.  And  so  on. 
Every  new  idea  added  represents  a  new  requisite  in  the 
object  that  is  to  correspond.  The  more  you  require  in 
the  objects,  the  fewer  will  they  be  found. 

Once  more  take  the  term  animal.  What  is  its  com- 
prehension .J*  What  ideas  docs  it  imply  .^^  It  implies 
sensitive  orc^nnic  material  substance.  Diminish  the  com- 
prehension.  Take  away  the  term  sensitive.  You  have 
left   organic   material  substance.      At    once   you    have 


36 


THE    LAWS    OF    THOUGHT. 


widened  the  extension  so  as  to  take  in  the  whole  vege- 
table kingdom.  Diminish  comprehension  again.  Strike 
out  organic.  There  remains  material  substance.  The 
extension  is  widened  so  as  to  take  in  all  that  is  matter 
whether  organic  or  not.  Diminish  the  comprehension 
again.  Strike  out  material.  Substance  remains.  The 
extension  has  been  increased  so  as  to  reach  into  the 
spiritual  world. 


Article  VI.     Extension  of  Propositions  — 

Quality. 

Universal  —  Collective  —  Particular  —  Singular. 

62.  Extension.  We  have  just  spoken  of  extension  in 
the  abstract  as  contrasted  with  comprehension.  In  No. 
19  we  saw  that  the  same  idea  could  be  u.sed  with  varied 
compass  within  the  entire  range  of  its  extension.  It 
may  be  singular,  particular,  collective,  universal 

63.  The  Subject.  The  extension  of  a  proposition  de- 
pends upon  the  extension  or  compass  of  the  subject  as 
used  in  the  proposition.  The  proposition  is  named 
accordingly  singular,  particular,  collective,  universal. 
The  following  are  exam])les.  Singular:  This  man  is 
virtuous.  Particular:  Some  man  is  virtuous.  Some 
men  are  virtuous.  Collective :  The  crowd  is  orderly. 
Universal :  Angels  are  spirits. 

64.  N.B.  In  speaking  of  terms  and  propositions  we 
shall  often  not  make  a  distinction  between  singular,  col- 
lective and  particular,  but  shall  call  them  indifferently 
by  the  name  particular  as  representing  any  term  or 
proposition  that  is  not  universal. 


, 


JUDGMENTS,   PROPOSITION.'*. 


37 


65.  The  Predicate.  To  state  clearly  what  we  wish  to 
say  about  the  predicate,  let  us  take  four  propositions, — 
two  universal  and  two  particular,  —  and  let  one  of  each 
kind  be  an  affirmative  proposition ;  the  other,  a  nega- 
tive.    This  will  give  us,  for  instance,  the  following : 

1.  Cats  are  quadrupeds.     (Universal  Affirmative.) 

2.  Birds  are  not  quadrupeds*    (Universal  Negative.) 

3.  This  field  is  triangular,     (Particular  Affirmative.) 

4.  Some  roses  are  not  red,     (Particular  Negative.) 

66.  Universal  Affirmative.  The  first  proposition  is  uni- 
versal, because  its  subject  is  universal,  i.e.  taken  in  its 
entire  extension.  As  to  the  predicate,  quadruped,  we  do 
not  directly  allude  to  its  extension.  We  merely  assert 
that  the  idea  quadruped  enters  into  the  comprehension 
of  the  idea  cat.  And  as  cat  here  is  universal,  taking  in 
each  and  every  cat,  we  do  state  that  quadruped  is  at 
least  coextensive  with  cat.  But  we  do  for  a  fact  know 
that  quadruped  has  a  wider  extension  than  cat,  that  cat 
covers  only  a  part  of  the  extension  of  quadruped.  Only 
some  quadrupeds  are  cats.  Hence,  when  we  speak 
according  to  our  knowledge  and  say  that  all  cats  are 
quadrupeds,  we  wish  to  say  that  some  quadrupeds  arc  cats, 
or  the  idea,  cat,  extends  to  some  individuals,  not  to  all 
individuals  in  the  extension  of  quadruped.  Quadrupedy 
therefore,  in  the  discussion  of  the  proposition  is  to  be 
regarded  as  a  particular  term.  As  these  remarks  hold 
good  for  all  universal  affirmative  propositions  (one  class 
excepted),  we  formulate  the  law  :  TJic  Predicate  in  a  uni- 
versal affirmative  proposition  is  a  particular  term. 

67.  One  Exception.  The  one  exception  is,  when  the 
predicate  is  the  exact  essential  definition  of  the  subject. 
Thus  in  the  proposition,  Man  is  a  rational  a7iimal,  the 


! 


38 


THE    LAWS    OF    THOUGHT. 


predicate,  rational  animal,  is  the  essential  definition  of 
the  subject,  man.  It  is  synonymous  with  man.  Hence  it 
is  precisely  coextensive  with  the  subject.  We  can  say, 
Man  is  a  rational  ani)nal,  or  Rational  animal  is  man. 
But  thou<;h  we  say,  Cat  is  quadruped,  we  cannot  say, 
Quadruped  is  cat.  Quadruped  may  be  tif^er  or  elephant. 
Rational  animaly  however,  cannot  be  anything  but  man. 

68.  Universal  Negative.  In  the  second  proposition. 
Birds  are  not  quadrupeds,  the  subject  is  universal,  and 
hence,  too,  the  proposition.  By  denial  we  separate  the 
idea  quadruped  from  the  comprehension  of  the  idea  bird. 
So  that  wherever  the  idea  bird  is  applicable,  in  its  entire 
extension,  there  the  idea  quadruped  is  excluded.  Now, 
knowin<;  that  quadruj^ed  can  have  its  own  extension,  the 
proposition  implies  that  bird  and  quadruped  extend  to 
two  distinct  classes  of  individuals.  To  say  that  birds  are 
not  quadru[)eds  is  the  same  as  saying  that  no  individual 
bird  is  a  quadruped.  Not  one  bird  can  be  found  in  the 
class  quadruped.  Not  one  quadrui)ed  can  be  found  in 
the  class  bird.  If  it  could,  some  bird  would  be  a  quad- 
ruped. What  is  this  but  to  exclude  quadrupeds  in  its 
entire  extension,  that  is,  as  a  universal,  from  the  entire 
extension  of  the  subject.?  As  the  same  remarks  hold 
good  for  all  universal  negative  propositions,  we  formulate 
the  law  :  The  Prcdieate  in  a  universal  negative  proposi- 
tion is  a  universal  term. 

69.  Particular  Affirmative.  In  the  third  proposition, 
This  field  is  triangular,  the  subject  is  particular.  Hence 
the  proposition  is  particular.  Referring  to  our  knowl- 
edge of  things,  we  shall  find  that  the  predicate,  triangu- 
lar, is  used  in  a  particular  sense.  We  do  not  predicate 
of  this  field  all  that  is  or  may  be  triangular,  the  entire 


JUDGMENTS,   PROPOSITIONS. 


39 


\ 


extension  of  triangular ;  but  only  this  particular  case  of 
triangular.  This  field  is  one  of  the  things  embraced  in 
the  extension  of  triangular.  Triangular,  hence,  is  used 
in  the  particular  sense.  These  remarks  hold  good  for 
every  particular  afifirmative  proposition.  Hence  the 
law  :  The  Predicate  in  a  particular  affirmative  proposi- 
tion is  a  particular  term. 

70.  Particular  Negative.  In  the  fourth  proposition. 
Some  roses  are  not  red,  the  extension  of  the  subject,  only 
some  roses,  is  particular.  Hence  the  proposition  is  par- 
ticular. The  predicate  red,  however,  is  used  in  the 
universal  sense.  We  aflfirm  that  redness  is  not  found 
in  the  comprehension  of  some  certain  roses.  No  one  of 
these  some  certain  roses  is  to  be  found  in  the  entire 
extension  of  things  that  are  red.  We  separate  the 
entire  extension  of  things  that  are  red  from  these  some 
certain  roses.  Hence,  in  our  denial  of  red  as  applicable 
to  some  roses,  we  use  it  in  its  entire  extension,  or  as  a 
universal.  These  remarks  hold  good  for  every  particu- 
lar negative  proposition.  Hence  the  law:  The  Predi- 
cate in  a  particular  negative  proposition  is  a  universal 
term. 

71.  Two  Laws.  Now  let  us  put  the  four  laws  together 
and  make  two  of  them.  The  first  and  third  will  give  us 
this  :  TJie  predicate  in  an  affirmative  proposition  is  used 
as  a  particular  term,  i.e.  according  to  pa^'t  of  its  extension. 

The  second  and  fourth  law  will  give  us  this  :  The  pred- 
icate in  a  negative  proposition  is  used  as  a  universal 
term,  i.  e.  according  to  its  entire  extension. 

72.  Affirmative  and  Negative.  We  have  not  thought 
it  necessary  to  state  explicitly  heretofore  that  every 
proposition  must  be  either  affirmative  or  negative.     For 


40 


THE    LAWS    OF   THOUGHT. 


all  needs,  up  to  the  present,  this  was  suffieiently  implied 
in  the  definitions  oi  judgment  Tin^  proposition. 

73.   Negrative  Particle.     We  call  attention  now  to  the 
fact  that,  in  the  negative  proposition,  the  negative  par- 
ticle need  not  necessarily  stand  between  the  subject  and 
the  i)redicate.     To  say.  Birds  arc  not  quadrupeds,  is  the 
same  as  saying.  No  bird  is  a  quadruped.     Both  are  neg- 
ative  and   are   understood  as  such.      We   have   not  To 
question  the  arbitrary  constructions  of  language.     Still 
be  it  understood  that,  in  order  to  have  a  negative^ proposi- 
tion, the  language  must  be  capable  of  such  construction 
that  the  negative  particle  not  may  be  construed  with  the 
copula,  is,  arc,  so  as  to  form  with  it  one  piece  that  shall 
be,  not  as  a  link  between  subject  and  predicate,  but  as 
a  wall  of  separation.     This  is  the  case  in  the  example 
given  above.     But  the  following  proposition  is  affirma- 
tive :   Not  to  complain  in  adversity  is  a  mark  of  a  great 
soul.     We  may  indeed  say,  To  complain  in  adversity  is 
not  a  mark  of  a  great  soul;  but  the  two  proi)ositi()ns  are 
not  identical  in  meaning,  for  we  turn  the  predicate  from 
a  particular  into  a   universal.     However,  we  may  say, 
A  mark  of  a  great  soul  is  not-to-complain-in-adversity. 
Here  the  negative  particle,  though  next  to  the  copula,  is, 
does  not  form  one  piece  with  it :  it  forms  a  piece  of  the 
predicate.     The  proposition  is  affirmative. 

^  74.  Quantity  and  Quality.  The  extension  of  a  propo- 
sition, universal,  particular,  etc.,  is  referred  to  as  its 
quantity.  The  form,  affirmative  or  negative,  is  referred 
to  as  its  quality. 


\ 


JUDGMENTS,    PROPOSITIONS.  41 

Article  VII.     Related  Propositions. 
Conversion  —  Equivalence  —  Opposition. 

75.  Three  Relationships.  We  now  pass  on  to  consider 
the  relations  that  may  exist  between  certain  propositions. 
The  relation  between  two  propositions  —  when  there  is 
any  relation  at  all  — will  be  one  of  convertibility,  of 
equivalence  or  of  opposition. 

76.  Conversion.     A  proposition  is  said  to  be  converti- 
ble into  another  when  the  subject  can  be  made  predicate 
and  the  i)redicate  subject  without  loss  of  truth  in  the  new 
proposition.    Thus  the  proposition,  No  man  is  an  angel, 
IS  convertible  into  No  angel  is  a  man.     There  are  th'i-ee 
ways   of  converting  propositions.      We   may  keep  the 
quantity   and   quality   unchanged;    or  we   may  change 
quantity  only;    or  we  may  change  quality  only.      The 
first  is  called  simple  conversion ;  the  second,  conversion 
per  accidens;    the    third,    conversion   by  contraposition. 
Without    minding    these    traditional    names,    we   shall 
exemplify  the  three  conversions. 

Quantity  and  quality  unchanged.  This  conversion 
may  take  place  in  propositions  where  subject  and  predi- 
cate are  both  universal  or  both  particular  — that  is,  in 
universal  negative  and  particular  affirmative ;  as  also,'  in 
propositions  where  the  predicate  is  the  essential  defini- 
nition  of  the  subject,  since  the  two  are  coextensive. 
Thus,  No  man  is  an  angel  is  convertible  into  No  angel 
IS  a  man.  T his  field  is  square  is  convertible  into  This 
square  thing  is  afield  Man  is  a  rational  animal  is  con- 
vertible into  The  rational  animal  is  man. 

Quantity  changed     This  kind  of  conversion  may  be 
applied  to  universal  affirmative  and  universal  negative 


42 


THE    LAWS    OF    THOUGHT. 


propositions.  In  the  universal  affirmative,  All  plants  arc 
substances,  the  predicate  is  particular.  If  nx  make  it 
subject,  we  have  Some  substances  an-  plants.  The  uni 
versa!  negative,  No  man  is  an  angel,  we  saw  above  may 
be  cc,nverted  mto  No  angel  is  a  man.  This  being  un^ 
vcrsal,  apphes  to  each  individual  in  the  extension  of  the 
subject ;  hence  we  have.  This  angel  is  not  a  man. 

Quahty  changed.     This  kind  of  conversion   may  be 

ne"  tJ"  Th'"  """^'■"'  ^'''^''  ^""  ^he  particular 
ncgat  ve.     The  universal  affirmative.  Cats  are  ,j,uulrn- 

Pcjls,  tels  us  that  cats  are  altogether  within  the  e.x  ension 
of  quadruped.  Outside  of  the  extension  of  quadruped 
cats  are  not  to  be  looked  for.  Hence  the  proposition  {. 
convertible  mto  What  is  not  gnaJn.peU  is  not  a  cat  In 
the  ,,art,cular  negative.  Some  roses  arc  not  red,  red  is 
universal  m  its  extension.  Hence  outside  of  the  exten 
s.on  of  red  there  are  some  roses;  or.  Some  things  not 
rctt  arc  roses.  '^ 

77  Equivalence  or  EquipoUence.  A  proposition  is  said 
toh^  apnvalent  to  (equal  in  value)  or  equipollent  with 
(equal  in  weight)  another  when  it  means  the  same  thiiu^ 
as  the  other  there  being  no  conversion  of  subject  and 
predicate.  A  ,>roposition  is  turned  into  its  equipollent 
m  venous  ways  by  the  use  of  the  negative  plrticle. 
1  hus,  Lvcry  man  is  mortal  is  equivalent  to  No  man  is 
not  mortal,  etc. 

78    Opposition.     To  explain  what  is  meant  by  o,,,,osi- 
^on,  let  „s  take   the  universal  affirmative  propoLlion 

^ZJH^l  "  T-      '"  "''"^■''  "'''■"-'•^  '"^  ^°"''-^dict  this 
It  wo, Id  be  sufficient  to  say.  Some   man  is  not  just 

Now  take  the  universal  negative  proposition.  No  man 

just.     To  contradict  this  it  is  enough  to  say.  Some 


I 


JUDGMENTS,   PROPOSITIONS. 


43 


( 


i 


man  is  just.  We  have  in  both  cases  an  opposition 
between  a  universal  and  a  particular,  an  affirmative  and 
a  negative.  There  is  opposition  in  both  quantity  and 
quality.  The  opposition  is  one  of  contradiction.  Propo- 
sitions so  related  are  called  contradictories.  Both  cannot 
be  true,  simultaneously ;  nor  can  both  be  false,  simulta- 
neously. If  it  be  true  that  all  men  are  just,  then  it  is 
false  that  some  man  is  not  just. 

Opposition  in  quality  only.  When  two  universal  prop- 
ositions are  opposed  in  quality,  i.e.  one  being  affirm- 
ative, the  other  negative,  as.  All  men  arc  just  and  No 
men  arc  just,  there  is  not  merely  a  contradiction  of  a 
sweeping  statement.  There  is  a  sweeping  statement  to 
the  contrary.  The  contradiction  covers  each  individual 
in  the  extension  of  the  opposite  proposition.  The  oppo- 
sition is  one  of  contrariety.  The  propositions  are  called 
contraries.  Both  cannot  be  true  at  the  same  time,  be- 
cause each  one  contradicts  every  individual  case  of  the 
other.  However,  both  may  be  false.  They  may  both 
claim  too  much  in  opposite  directions. 

The  particular  propositions  imj)lied  in  these  two  uni- 
versals,  that  is,  the  particulars.  Some  man  is  just  and 
Some  man  is  not  just,  as  opposed  to  one  another  in 
quality,  are  called  subcontraries.  Both  may  be  true, 
since  their  contradictories,  the  universals,  may  both  be 
false,  may  both  assert  too  much.  Both  particulars, 
however,  cannot  be  false  ;  for  if  both  were  false,  then 
their  contradictories,  the  universals,  would  both  be  true. 

Opposition  in  quantity  only.  This  is  the  opposition 
between  a  universal  and  particular  affirmative  or  a 
universal  and  particular  negative,  as.  All  men  are  just 
and  Some  man  is  just ;  or  No  man  is  just  and  Some 
man  is  not  just.     There  is  in  reality  no  opposition  here. 


44 


THE    LAWS    OF    THOUGHT. 


The  particular  is  implied  in  the  universal.  It  is  a 
subaltern  of  the  universal.  Hence,  for  the  sake  of  a 
name,  propositions  so  related,  the  universal  and  its 
implied  i)articular,  are  called  subalterns.  If  the  uni- 
versal is  true,  the  particular  is  true.  If  the  universal 
is  false,  the  particular  may  still  be  true.  From  the  truth 
or  falsity  of  the  particular  we  can  form  no  judgment 
about  the  truth  or  falsity  of  its  universal. 

79.    Diagram.     Now  look  at  the  following  diagram  : 

CONTKAKV. 
I.  All  men  are  just  (6^;//r'.  Aff.).  2.  No  man  is  just  {Univ.  N,<;.). 


r 

H 


O 


> 

X 

r 

H 

W 
7i 

'^^^ 

25 

3.  Some  man  is  just  {Pari.  Aff.).  4.  Some  man  is  not  just  {Part.  Neg.). 

SirnCONTRAKV. 

I   and  2  are  contraries;    3  and  4  are  subcontrarics ; 

1  and  4,  also  2  and  3,  are  contradictories ;    i  and  3,  also 

2  and  4,  are  subalterns  (i  and  2  being  called  subalternant, 

3  and  4  their  subalternates). 

It  is  clear  that  if  i  is  true,  3  is  true;  and  that  if  2  is 
true,  4  is  true.  But  we  cannot  conclude  from  3  to  i  nor 
from  4  to  2. 

I  and  4  cannot  be  both  false.  One  must  be  true,  and 
the  other  false.     The  same  is  to  be  said  of  2  and  3. 

3  and  4  may  be  both  true,  or  one  true  and  the  other 
false,      l^oth  cannot  be  false. 


i 


!» 


\ 


CHAPTER   IV.     REASONING,  ARGUMENT. 


Article  I.     The  Syllogism. 

Argument  —  The  Syllogism  —  Analysis  of  Argument  —  Middle  and 

Extremes. 

80.  Reasoning  and  Argument.  We  have  seen  how  the 
idea  is  the  element  of  the  judgment,  and  thus  the  term, 
the  element  of  the  proposition.  We  have  now  to  see 
how  an  argument  is  constructed  out  of  propositions. 
We  defined  Reasoning  (11)  to  be  an  act,  or  a  series  of 
acts,  by  which  the  mind  compares  the  truths  expressed 
by  two  judgments,  and  in  that  comparison  perceives 
implied  a  third  truth,  which  it  accordingly  expresses 
mentally  in  a  third  judgment.  This  process,  we  said, 
regarded  as  mere  mental  working,  is  called  reasoning. 
Regarded  as  knowledge  contained  in  the  third  judgment, 
pronounced  as  having  been  implied  in  the  two  others, 
we  called  it  inference  or  argument.  The  propositions 
which,  taken  together,  represent  in  language  the  knowl- 
edge and  its  process,  we  also  called  argument.  We 
shall  use  the  word  argnnient  in  this  latter  sense. 

81.  Styles  of  Argument.  There  are  indeed  many  com- 
binations of  propositions  which  are  used  as  language- 
representations  of  the  process  of  reasoning,  many  styles 
of  argument.  Different  names  are  given  to  them,  accord- 
ing to  the  variety  of  structure.     We  have  the  Syllogism, 

45 


} 


46 


THE  LAWS  OF  THOUGHT. 


REASONING,  ARGUMENT. 


47 


the  Ent/iymnfte,  the  Sorites,  the  Poly  syllogism,  the  E/>i- 
chirem,  the  Dilemma.  All,  however,  are  reducible  to  the 
syllogism,  which  is  the  nearest  approach  language  can 
make  towards  exhibiting  th;^  working  of  the  mind  in 
reasoning.  Not  that  we  always,  or  usually,'  argue,  in 
speaking  or  writing,  with  completed  syllogisms.  We 
abbreviate.  However,  we  must  study  the  syllogism  in 
its  completeness.  We  begin  with  it.  A  few  words  at 
the  end  of  this  chapter  will  then  suffice  to  exi)lain  the 
other  styles  of  argument. 

82.  The  Syllogism.  The  syllogism  is  an  argument 
made  up  of  three  propositions  so  connected  that  if  the 
first  two  be  admitted,  the  third  must,  likewise,  be 
admitted.     Thus, 

Evct'ij  jt/anf  is  a  substance: 
lint  the  verltena  is  a  plnnt. 
Therefore,       Tfie  verbena  is  a  safpstanre. 

83.  Antecedent;  Consequent;  Premisses.  The  first  two 
propositions  taken  together  are  called  the  antecedent. 
The  third  proposition  is  called  the  consequent.  In  the 
antecedent  the  evidence  is  stated.  In  the  consequent 
the  verdict  is  given.  The  two  propositions  of  the  ante- 
cedent are  commonly  called  premisses  (put  before).  The 
first  is  called  the  major  premiss;  the  second,  the  minor 
premiss.  For  brevity's  sake  they  are  styled  the  major 
and  the  minor.  The  original  meaning  of  mtrjor  and 
mi;wr,  and  the  reason  for  the  use  of  the  terms,  will  be 
explained  in  the  next  article. 

84.  Consequence.  If  the  consequent  does  really  fol- 
low from  the  premisses,  we  have  what  is  called  a  conse- 
quence, by  which  we  mean  that  the  assertion  contained 


in  the  consequent  is  a  consequence  of  what  was  laid 
down  in  the  premisses.  If  an  argument  is  proposed  to 
us  in  which  the  consequent  does  not  follow  as  a  conse- 
quence,  the   argument    must    be   regarded    as   faulty. 

Hence, 

{a)  If  both  the  premisses  be  true,  and  the  argument 
be  rightly  constructed,  the  consequent,  called  also  the 
conclusion,    must    be    true:    the   consequent   must    be 

admitted. 

(/;)  The  conclusion,  or  consequent,  may  indeed  be  a 
true  proposition,  as  stated,  and  taken  by  itself  ;  and,  still, 
on  account  of  a  flaw  in  the  structure  of  the  argument,  it 
may  not  really  follow  from  the  premisses.  In  this  case 
we  may  admit  it  as  an  independent  proposition.  We 
admit  the  consequent,  but  we  deny  the  consequence, 

85.  Axioms.  Wc  repeat  here  two  axioms  stated  in 
No.  II.  They  are  the  bases  upon  which  every  argu- 
ment must  rest.  If  the  conclusion  is  an  affirmative 
proposition  the  argument  rests  upon  this  axiom :  /;/  the 
sense  in  which  two  things  are  the  saine  as  a  third  things 
in  the  same  sense  are  they  the  same  as  one  another.  If 
the  conclusion  is  a  negative  proposition,  the  argument 
rests  upon  this  axiom  :  In  the  sense  in  which  two  things 
are,  the  one  the  same  as  a  third  thing,  the  other  differ- 
ent from  it,  in  the  same  sense  are  they  different  from  one 
another. 

86.    Analysis  of  Argument.     Now  look  at  the  argument 
given  above,  namely : 

J  Every  plant  is  a  substance  {Major  Premiss). 
Antecedent        ^  ^^^^  ^^^^  verbena  is  a  plant  (Miftor  Premiss). 

Consequent  or  J  Therefore,  the  verbena  is  a  substance  (Conse- 
CoNCLUSiON      (  quence). 


U  i 


48 


THE  LAWS  OF  THOUGHT. 


REASONING,  ARGUMENT. 


You  will  find 

1.  That  it  contains  but  three  terms,— //,^///,  substance, 
verbcua.  ^ 

2.  That  one  of  the  terms,  /A?///,  occurs  twice  in  the 
premisses,— once  in  the  major,  and  once  in  the  minor. 

3.  That  the  two  other  terms,  substance,  verbena,  occur 
each  once  in  the  premisses,  one  in  the  major,  and  one  in 
the  minor;  and  that  they  both  occur  in  the  conclusion. 

4-    That  the  term//<r/;//  is  not  found  in  the  conclusion. 

5.  That  thus  each  term  occurs  twice  in  the  ar^^ument. 

6.  That  the  term  />/ant,  which  occurs  twice  in  the 
premi.s.ses,  is  there  compared  with  the  two  others;  with 
one  in  the  major,  with  the  second  in  the  minor. 

7-  That  a  certain  relationship  havin<r  been  discovered, 
in  the  premisses,  between  verbena  and  substance,  by 
means  of  the  aforesaid  comparison,  this  relationship  is 
declared  in  the  conclusion. 

87.  Middle  and  Extremes.  The  term  that  is  used  as  a 
standard  of  comi)aris()n  between  the  two  others  is  called 
the  mi(iii/e  term  ;  or  for  brevity,  the  miihile :  the  two 
others  are  called  the  extreme  terms  or  the  extremes,  one 
the  major  and  the  other  the  minor  extreme.  We  shall 
have  to  speak  of  this  subject  presently. 


Article  1 1.     Figures  and  Moods  of  the 

Syllogism. 

Major  and  Minor  Premiss  —  Major  and  Minor  Extreme  —  Middle 

Term. 

88.  Major ;  Minor ;  Middle.  We  spoke,  in  the  last  arti- 
cle, of  major  and  minor  premiss,  major  and  minor  ex- 
treme, and  of  the  middle.     We  called  the  first  premiss 


49 


the  major,  and  the  second  premiss  the  minor,  and  we 
shall  continue  to  call  them  so.  But  the  first  premiss  is 
not  always  really  the  major,  in  the  original  meaning 
attached  to  the  word  ;  nor,  in  the  same  original  meaning, 
is  the  second  always  the  minor.  According  to  the  orig- 
inal use  of  the  words,  the  major  premiss  is  the  premiss  in 
which  the  middle  is  compared  with  the  major  extreme ; 
and  the  minor  premiss  is  the  one  in  which  the  middle 
is  compared  with  the  minor  extreme.  The  major  ex- 
treme is  the  one  whose  extension  is  greater  than  that  of 
the  middle.  The  minor  extreme  is  the  one  whose  exten- 
sion is  less  than  that  of  the  middle.  This  is  how  the 
middle  came  to  be  called  middle  ;  because,  its  extension 
is  between  the  extensions  of  the  two  other  terms. 

There  is  only  one  style  of  syllogism  in  which  the  mid- 
dle is  a  real  middle,  as  just  explained.  This  is  in  the 
most  obvious  style  of  construction  of  the  syllogism  (No. 
89)  ;  and  it  is  from  this  that  the  names  have  grown  into 
common  use,  and  are  applied  to  all  syllogisms,  in  the  same 
way,  regardless  of  construction.  We  call  the  premiss 
put  first,  the  major;  that  put  second,  the  minor:  and 
we  never  speak  of  the  extremes  as  major  and  minor. 
This  leads  us  to  the  question  of  figures  of  the  syllo- 


gism. 


By  Figures  are  meant  merely  the  various  combina- 
tions of  the  extremes  with  the  middle,  in  the  premisses. 

89.  First  Figure.  The  First  Figure  is  the  one  that  we 
have  just  spoken  of.  In  this,  the  middle  is  made  the 
subject  of  the  premiss  containing  the  major  extreme,  and 
this  premiss  is  placed  first :  it  (the  middle)  is  made  the 
predicate  of  the  premiss  containing  the  minor  extreme, 
and  this  premiss  is  placed  second.     Thus  : 


so 


THE    LAWS    OF    THOUGHT. 


Animals  are  living  heinr/s;  (Major  Premiss.) 
But  lions  are  animals.     (Minor  Tremiss.) 
Therefore,  J.iotis  are  living  beings. 

Here  the  middle,  aniuials,  has  less  extension  than 
living  bciuij^s  (major  extreme),  and  greater  extension  than 
lions  (minor  extreme).  The  following  squares  will  show 
how  one  is  included  in  the  extension  of  the  other,  and 
how  easily  the  argument  proceeds  on  that  account. 


LIVING  BEINGS 


ANIMALS 


LIONS 

Minor 

Extreme 


MiddU 


Major  Extreme 


As  our  argument  was  stated,  we  proceeded  within  the 
extension  of  living  beings  to  f^nd  animals,  and  then 
within  the  extension  of  animals  to  find  lions ;  thence  to 
conclude  that  lions  were  within  the  extension  of  living 
beings,  and  that  living  being  could  be  i)redicated  of  lion. 
The  minor  premiss  might  be  placed  first,  and  the  major 
premiss  second.     Thus  : 

lAons  are  animals; 
But  animals  are  living  beings. 
Therefore,  Lions  are  living  beings. 

In  this,  we  proceed  from  the  minor  extreme  up  through 
the  middle  to  the  major  extreme. 


REASONING,    ARGUMENT. 


51 


90.  Second  Figure.  We  remark,  again,  that  outside  of 
the  First  Figure,  what  we  call  middle  is  really  not  a 
middle,  in  the  true  sense,  but  only  in  the  sense  that  it  is 
taken  as  a  term  of  eomparison  between  two  other  terms. 
Still  we  keep  the  name,  middle ;  and  the  other  terms 
are  called  simply  the  extremes. 

In  what  we  call  the  Second  Figure,  the  middle  term  is 
used  as  predicate  in  both  premisses.     Thus : 


Therefore, 


Every  man  is  mortal; 
No  angel  is  mortal. 
No  angel  is  a  man. 


Here  mortal  is  the  middle.  Man  is  truly  minor  with 
reference  to  mortal.  But  we  cannot  say  that  Angel  is 
major  with  reference  to  mortal.  Angel  is  simply  ex- 
cluded by,  and  excludes,  mortal,  and  hence,  excludes 
the  minor  contained  in  mortal. 


MORTAL 

MAN 

91.  Third  Figure.  In  what  we  call  the  Third  Figure 
the  term  of  comparison  is  the  subject  of  both  the  first 
and  second  premiss.     Thus  : 


Therefore, 


Every  plant  is  substance; 
Every  plant  is  fnaterial. 
Some  substance  is  material. 


52 


THE  LAWS  OF  THOUGHT. 


REASONING,  ARGUMENT. 


53 


/I 


Here  the  term  plant  has  less  extension  than  either  of 
the  other  two.  The  meaning  of  middle  is  lost.  The 
extremes  are  both  major. 


Both  substance  and  material  cover  the  extension  of 
plant,  and  hence  partly  coincide,  i.e.  at  least  to  the 
extent  of  plant.  This  will  suffice  on  the  subject  of 
Figures. 

What  we  have  to  remember  is  this,  that  in  practice 
the  premiss  which  stands  first  we  shall  call  major;  the 
premiss  that  stands  second,  minor;  the  term  that  is 
used  as  the  standard  of  comparison,  middle ;  the  two 
other  terms,  extrejnes. 

92.  Moods  of  the  Syllogism.  By  moods  of  the  Syl- 
logism are  meant  the  various  combinations  that  may  be 
made  in  the  premisses,  of  universal,  particular,  affirma- 
tive and  negative  propositions.  We  should  derive  no 
practical  utility  from  a  discussion  of  the  sixty-four 
possible    combinations,    few    of    which    give    a    correct 


\ 


argument.  For  the  sake  of  a  completeness,  which  is 
not  necessary,  we  subjoin  the  following  remarks  on 
figures  and  moods. 

I.  There  is  a  Fourth  Figure,  which  is  little  used,  and 
which  it  is  well  to  avoid  in  argumentation.  In  it  the 
middle  is  made  predicate  of  the  major  proposition  and 
subject  of  the  minor. 

Every  tree  is  organic; 
Everything  organic  is  substance. 
Therefore,  Some  substance  is  a  tree. 

This,  it  will  be  noticed,  is  the  same  as  the  First  Figure 
with  the  position  of  subject  and  predicate  inverted  in 
the  conclusion,  and  the  proposition  accordingly  changed 
from  the  universal,  jEverj/  tree  is  a  substance,  to  the 
implied  particular. 

2.  If  now  we  take  the  four  kinds  of  propositions. 
Universal  Affirmative,  Universal  Negative,  Particular 
Affirmative  and  Particular  Negative,  and  make  all  the 
possible  combinations  of  them  that  can  be  made  in  each 
of  the  Four  Figures,  we  shall  find  that  there  are  sixteen 
possible  combinations  in  each  figure,  or  sixty-four  in 
all,  —  simply  regarding  the  position  of  the  middle  and 
taking  no  account  of  the  validity  of  the  conclusion. 
These  sixty-four  combinations  are  called  the  Moods  of 
the  Syllogism.  If  we  take  into  account  the  validity  of 
the  conclusion  as  proceeding  from  the  premisses,  we 
shall  find  that  only  nineteen  of  the  sixty-four  combina- 
tions make  correct  arguments.  These  nineteen  Moods 
are  thus  distributed  :  4  in  the  First  Figure ;  4  in  the 
Second  ;  6  in  the  Third ;  and  5  in  the  Fourth. 

We  shall  be  able  to  decide  upon  the  correctness  of  any 
combination  from  the  laws  of  the  syllogism  which  follow. 


I 


54  THE    LAWS    OF    THOUGHT. 

Article   III.     Laws  of  the  Syllogism. 

93.  Scope  of  the  Laws.  We  arc  now  prepared  to 
formulate  the  laws  which  must  govern  the  construction 
of  the  correct  .syllogism.  These  laws  have  reference  to 
the  number  of  terms,  the  extension  of  term.s,  the  place 
of  the  middle  term,  the  quantity  and  quality  of  premisses 
and  conclusion. 

94.  First  Law.  Three  Terms.  T/n^rc  viiist  be  three, 
and  only  threes  terms,  and  they  must  be  only  three  In 
meaning.  This  is  evident  from  what  has  been  said: 
that  the  conclusion  of  a  syllogi.sm  is  simply  a  declaration 
of  identity  or  difference  between  two  terms  (objectively), 
which  identity  or  difference  was  implied  by  the  compari- 
son of  these  terms  (objectively)  with  a  third  term  in  the 
premisses.  It  is  not  enough,  therefore,  to  have  the 
terms  three  in  mere  sound  or  written  appearance.  They 
mu.st  be  three  in  meaning  (objectively).  Our  rea.soning 
is  not  upon  sounds  of  the  voice  or  upon  printed  letters ; 
it  is  upon  that  which  is  represented  both  by  the  idea  and 
by  the  spoken  and  written  word.     If  we  say : 

Stores  are  tvareJtouses, 
Stores  can  be  eaten, 
Therefore,    Warehouses  can  he  eaten, 

we  have  three  terms  in  sound  and  writing  ;  but  we  have 
four  in  meaning;  and  thus  there  is  no  syllogism.  If 
we  say : 

Kye  -is  the  organ  of  sight, 

I  is  a  personal  pronouti^ 
Therefore,   The  organ  of  sight  is  a  jtersonal  j}rononn, 


reasoning,  argument. 


55 


{ 


ii 


the  terms  are  three  in  sound,  but  four  in  meaning,  as  in 
writing.     There  is  no  syllogism.     If  we  say : 

Andrew  Jackson  is  one  of  the  Presidents^ 
Franklin  Pierce  is  one  of  the  Presidents, 
Therefore,  Andrew  Jackson  is  Franklin  Pierce, 

we  have  four  terms,  in  meaning;    because,   One-of-the- 
Presidents  is  taken  in  two  dificrcnt  part ieu la r  senses. 

95.  Second  Law.  Extension  of  Extremes.  Neither  ex- 
treme may  have  a  greater  extension  in  the  conelusion  than 
it  had  in  the  premisses.  This  is  a  consequence,  or  an 
application,  of  the  first  law.  For  if  a  term  in  the  conclu- 
sion embraces  more  individuals  than  it  did  in  the  prem- 
isses, it  is  really  a  fourth  term,  because  it  stands  for 
something  not  meant  in  its  first  use.     In  the  following, 


Therefore, 


Tobacco  is  a  plant. 
Tobacco  is  narcotic. 
Plants  are  narcotic. 


the  term  plant,  as  predicate  of  an  affirmative  proposi- 
tion in  the  major,  is  a  particular  term  ;  whilst,  in  the 
conclusion,  as  subject  of  the  universal  proposition,  it  is 
taken  according  to  its  entire  extension.  There  are  four 
terms  :  hence  no  syllogism. 

96.  Third  Law.  Extension  of  the  Middle  Term.  The 
middle  term  must  be  used  once,  at  least,  according  to  its 
entire  extension,  i.e.  as  universal.  The  reason  :  for  if 
it  be  twice  a  particular,  each  use  may  embrace  totally 
different  sets  of  individuals,  totally  distinct  sections  of 
the  entire  extension.      This  would  give  two  different 


56 


THE    LAWS    OF    THOUGHT. 


meanings   for  the   middle,  and   hence,  four  terms.      If 

we  say : 

Tigers  are  anhnalHy 

Lions  are  animals , 

we  may  not  conclude 
Therefore,  Lions  are  tigers. 

The  middle  term,  aniiiiah,  is  twice  particular,  covering 
distinct  sections  of  the  entire  extension,  aniuials.  It  is 
really  two  tcniis. 

All  objection.  How,  then,  can  the  middle  term  be 
used  once  universally,  and  once  particularly  t  Will  not 
this  give  us  four  terms?  No;  because  what  is  said  of 
the  term  taken  universally,  i.e.  standing  for  all  individ- 
uals, and  for  each  and  every  individual  in  the  extension, 
can  also  be  said  of  this  or  that  individual  taken  sepa- 
rately.    An  example : 


Therefore, 


Spirit  is  indi risible  ; 
The  soul  is  spirit. 
The  soul  is  indivisible. 


In  the  major,  s/>irit  is  universal.  We  say  that  d// 
spirits  are  indivisible ;  hence,  that  each  particular  spirit 
is  indivisible.  In  the  minor,  we  simply  call  one  particu- 
lar spirit  by  its  name.  In  the  major  we  said  any  spirit. 
In  the  minor  we  make  the  choice  that  has  been  offered 
us  directly  in  the  major.     There  are  only  three  terms. 

Of  course  the  middle  may  be  used  twice  universally. 
In  this  case,  both  premisses  will  have  to  be  affirmative, 
and  the  conclusion  will  be  particular.     Thus : 


Therefore, 


All  fishes  are  sensitive; 

All  fi sites  are  shy. 

Some  things  sensitive  are  shy. 


REASONING,   ARGUMENT. 


57 


In  these  premisses  the  extremes  are  predicates  of  affir- 
mative propositions,  and  hence  are  particular.  There- 
fore, by  the  second  law,  they  must  have  a  particular  ex- 
tension in  the  conclusion.  This  last  example  belongs  to 
the  Third  Figure. 

97.  Fourth  Law.  Place  of  the  Middle  Term.  T/ie  mid- 
dle term  must  not  be  found  in  the  conclusion.  This  is 
evident  from  the  nature  of  the  syllogism.  Two  terms 
are  compared,  separately  in  the  premisses,  with  a  third 
term,  in  order  that  their  identity,  or  disparity,  may  be 
expressed  in  the  conclusion;  the  middle  term  being 
rejected,  after  its  use  as  a  standard  of  comparison. 

98.  Fifth  Law.  Affirmative  Conclusion.  Two  affirma- 
tive premisses  demand  an  affirmative  conclusion.  For  if, 
in  the  premisses,  we  implicitly  affirm  the  identity  of  the 
extremes,  we  cannot  deny  that  identity,  explicitly,  in  the 
conclusion. 

99.  Sixth  Law.  Negative  Conclusion.  O^ic premiss  affir- 
mative and  one  premiss  negative  demand  a  negative 
conclusion.  For,  in  the  premisses,  we  implicitly  deny 
identity  between  the  extremes,  by  declaring  that  one  is 
identical  with  the  middle,  and  that  the  other  is  not. 
Hence  we  have  but  to  deny  their  identity,  explicitly,  in 
the  conclusion. 

100.  Seventh  Law.  No  Conclusion.  From  tzvo  fiegativc 
premisses  zue  can  draw  no  conclusion.     If  we  say, 

Scipio  is  not  a  carjienter, 
Scipio  is  not  a  Russian, 

there  is  no  conclusion  to  be  drawn.      Wc  have  done 
nothing  but  to  place  Scipio  outside  the  extension  of  the 


58 


THE  LAWS  OF  THOUGHT. 


REASONING,  ARGUMENT. 


59 


two  extremes ;  but  there  is  nothing  from  which  to  infer 
whether  there  be,  or  be  not,  Russians  among  the  car- 
penters, or  carpenters  among  the  Russians.     All  we  can 


Carpenters 


Russians 


say  is  what  has  been  affirmed  explicitly,  that  Scipio  is 
neither  a  Russian  nor  a  carpenter. 

The  same  holds  if  the  premisses  are  two  negative  uni- 
versal propositions.  All  the  terms  will  be  universal. 
The  middle  term,  in  its  entire  extension,  will  be  outside 
the  entire  extension  of  each  extreme. 

No  star  is  an  elephatit; 

Xo  elephant  is  a  wheelbarrow, 

Xo  conclusion, 

101.  Eighth  Law.  No  Conclusion.  From  two  particu- 
lar premisses  we  can  draw  no  conehision.  For  they  will 
be  either,  i,  both  negative;  or  2,  both  affirmative;  or  3, 
one  affirmative  and  one  negative. 

First  case:  both  7iegative.  This  is  settled  by  the 
seventh  law. 

Second  case:  both  affirmative.  In  this  case  the  sub- 
jects are  particular,  as  we  have  particular  propositions ; 
and  the  predicates  are  j)articular  because  the  proposi- 
tions are  affirmative  (No.  71).  Hence  the  middle  term 
is  not  taken  once  universally,  and  the  third  law  is 
broken. 

Third  case :  one  affirmative  and  one  negative.  Then, 
according  to  the  sixth  law,  the  conclusion  will  have  to 


'' 


be  negative.  The  predicate  of  the  conclusion  will  thus 
be  universal  (No.  71).  As  this  predicate  is  one  of  the 
extremes,  it  must,  by  the  second  law,  be  universal  in  the 
premisses.  But  in  the  premisses  there  is  only  one  place 
for  a  universal  term ;  that  is,  as  predicate  of  the  negative 
premiss.  The  particular  affirmative  premiss  cannot  have 
a  universal  term,  and  the  subject  of  the  particular  nega- 
tive premiss  must  be  particular.  Now  if  this  one  place 
in  the  premisses  where  a  universal  term  can  be,  be  taken 
by  one  of  the  extremes,  the  middle  term  will  not  be, 
cannot  be,  used  universally  at  all.  Hence  this  third 
case  is  an  impossibility,  and  the  eighth  law  holds. 

We  must  here  make  an  exception  for  the  case  where 
both  premisses  are  singular.  In  this  case  there  may  be 
a  conclusion.     Thus : 


Therefore, 


Mars  is  a  j}lanet; 

Mars  is  uninhabited. 

One  2)lanet  is  uninhabited. 

The  reason  is  that  the  term,  Mars,  being  applicable 
to  one  individual  only  must  be  used  in  its  entire  exten- 
sion, and  hence,  as  subject  in  both  premisses,  has  the 
value  of  a  universal :  so  that  the  two  premisses  may  be 
treated  as  universals. 

102.  Ninth  Law.  Particular  Conclusion.  If  one  premiss 
be  particular^  the  conclusion  must  beparticidar.  Of  course, 
by  the  eighth  law,  one  premiss  must  be  universal.  The 
possible  cases  with  one  premiss  universal,  and  one  par- 
ticular, are : 

1.  With  both  premisses  affirmative; 

2.  With  one  premiss  affirmative,  the  other  negative ; 
and  in  the  second  case  we  have  an  alternative.  We 
may  take  a  universal  affirmative  and  a  particular  nega- 


6o 


THE  LAWS  OF  THOUGHT. 


REASONING,  ARGUMENT. 


6l 


tive ;  or  we  may  take  a  universal  negative  and  a  par- 
ticular affirmative. 

1.  Making  both  premisses  aflfirmative,  we  shall  have, 

Univkksal   Affirmative   (with  subject  universal  and  predicate 

particular)  ; 
pARTicirLAK  Affirmative  (witli  subject  particular  and  predicate 

particular). 

There  is  but  one  place  for  a  universal  term.  This 
must  be  for  the  middle  {Third  Laiv).  The  extremes 
are  both  particulars  in  the  premisses.  Hence  the  subject 
of  the  conclusion  must  be  particular  {Second  Lazc')'y  and 
the  conclusion,  a  particular  proposition. 

2.  Making  one  premiss  negative  and  one  affirmative, 
we  shall  have  either 

Universal  Affirmative  (with  subject   universal  and  predicate 

l)articular)  ; 
Particular     Neoative    (with    subject    particular  and   predicate 

universal) . 

Or, 

Universal     Neoative    (with    subject    universal   and    predicate 

universal)  ; 
Particular   Affirmative  (with  subject  particular  and  predicate 

particular). 

In  either  case  there  are  two  places  for  a  universal. 
One  place  must  be  for  the  middle  {Third  Lau^.  The 
other  place  will  be  for  the  extreme  which  is  predicate  of 
the  conclusion ;  the  conclusion  being  negative,  since 
one  premiss  is  negative.  The  subject  of  the  conclusion 
must  therefore  be  an  extreme,  used  particularly  in  the 
premisses.  It  must  be  particular  in  the  conclusion 
{Second  Lazu),  and  will  make  the  conclusion  a  particular 
proposition. 


103.  Caution.  Here  we  leave  the  laws  of  the  syllo- 
gism. Certain  correct  syllogisms  may  be  adduced  which 
may  seem  to  contravene  the  laws.  But  if  the  propo- 
sitions of  the  syllogisms  thus  presented  be  examined, 
it  will  be  seen  that  certain  propositions,  apparently 
particular,  are  really  universal ;  and  certain  propositions, 
apparently  negative,  are  really  affirmative,  or  vice  versa. 
But  let  it  be  kept  in  mind  that  we  reason  not  with  mere 
words  as  they  sound  or  appear  on  paper,  but  with  what 
they  stand  for ;  and  words,  by  tricks  of  grammar,  may 
be  made  to  obscure  a  thought  in  the  presentation.  In 
the  same  way,  syllogisms  with  ill-drawn  conclusions 
may  be  made  to  appear  in  keeping  with  the  laws.  But 
study  the  sense  of  the  propositions. 


Article  IV.     Some  Species  of  the  Syllogism. 

Conditional  —  Conjunctive  —  Disjunctive. 

104.  Simple  and  Compound  Syllogisms.  Wc  have  hith- 
erto, for  the  sake  of  clearness,  given  examples  of  syllo- 
gisms composed  of  simple  categorical  propositions  only. 
Such  syllogisms  are,  as  their  component  propositions, 
called  simple.  One  compound  premiss  is  sufficient  to 
make  the  syllogism  compound  and  equal  to  as  many 
simple  syllogisms  as  there  are  simple  categorical  propo- 
sitions compounded  into  that  premiss.  We  do  not 
propose  to  treat  of  compound  syllogisms.  We  should 
never  end.  Attention  is  called  here  to  three  complexi- 
ties in  the  syllogism,  to  which  we  alluded  in  No.  49. 

105.  Conditional  Syllogisms.  In  these  the  major  is  a 
conditional  proposition  (46);    for  instance,  this,  If  they 


62 


THE    LAWS    OF    THOUGHT. 


are  studying  logic,  they  arc  training  their  minds.  The 
first  member  of  the  conditional  proposition  is  called  the 
condition  ;  the  second,  the  consequent.  The  minor  may 
affirm  the  condition  categorically  : 

They  are  stutlying  logic. 

Then  the  conclusion  must  affirm  the  consequent  cate- 
gorically : 

Thvij  are  training  their  minils. 

Or  the  minor  may  deny  the  consequent : 

They  are  not  training  their  minds. 

Then  the  conclusion  denies  the  condition : 

They  are  not  studying  logic. 

Note,  i  .  The  denial  of  the  condition  will  not  necessitate  the 
denial  of  the  consequent.  This  (the  consequent)  may  be  true  for 
other  reasons.  In  the  present  instance  they  might  be  studying 
grammar  or  geometry  without  logic ;  and  they  would  still  be  train- 
ing tlieir  minds. 

2.  Hence  affirmation  of  the  consequent  does  not  always  necessi- 
tate affirmation  of  the  condition.  There  may,  as  we  said,  l)e  other 
conditions  from  which  it  (the  consequent)  would  follow.  They  may 
in  the  present  instance  be  training  their  minds  by  studying  other 
matters  than  logic. 

106.  Conjunctive  Syllog^isms.  In  these,  two  incompati- 
ble propositions  are  proposed  in  the  major  by  means 
of  a  conjunctive  proposition  (47).  The  minor  denies 
one,  and  the  conclusion  affirms  the  other.      Mxample: 

No  man  can  spend  all  his  money  on  drink  and  still 

support  his  family; 
Hut  lie  spends  all  his  money  on  drink. 

Therefore, 

He  does  not  support  his  family. 


REASONING,   ARGUMENT. 


63 


What  we  said  about  looking  into  the  meaning  of  the 
proposition  and  not  being  deceived  by  tricks  of  construc- 
tion is  of  service  here.  The  conjunctive  proposition  is 
really  equivalent  to  a  conditional,  thus,  If  a  man  spends 
all  his  money  on  drink,  he  is  tinable  to  support  his  family; 
and  with  regard  to  affirmation  and  denial  of  condition 
and  consequent  must  be  treated  as  such. 

107.  Disjunctive  Syllogisms.  In  these  the  major  puts 
all  the  alternatives  of  a  case  in  the  disjunctive  proposi- 
tion (48).  If  the  minor  makes  choice  of  one,  the  conclu- 
sion will  be  the  denial  of  all  the  others.  If  the  minor 
denies  all  but  one,  that  one  will  be  affirmed  in  the 
conclusion,  etc. 

Example  :  He  is  either  just  fifty  or  under  fifty  or  past 

fifty ; 

But  he  is  just  fifty  ; 
Therefore,  He  is  neither  under  fifty  nor  jmst  fifty  : 
Or  But  he  is  neither  under  fifty  nor  past  fifty  ; 

Therefore,  He  is  just  fifty : 
Or  But  he  is  not  just  fifty  ; 

Therefore,  He  is  either  under  fifty  or  past  fifty. 

In  the  last  case,  as  we  have  three  possibilities,  and  the 
minor  denies  one  only,  the  two  others  remain  as  a  dis- 
junctive proposition  in  the  conclusion.  This  form  of 
syllogism  may  also  be  reduced  to  the  conditional  with 
one  member  positive  and  the  other  negative.  If  he  is 
under  fifty,  he  is  neither  just  fifty  nor  past  fifty. 

The  conjunctive  syllogism  is  useful  in  controversy  and 
investigation.  But  it  is,  at  the  same  time,  capable  of 
treacherous  application  for  the  spread  of  error  in  history 
and  physical  science,  by  the  use  of  disjunctive  majors 
which  are  not  complete.     The  disjunction  should  state 


I 


64 


THE    LAWS    OF    THOUGHT. 


all  the  possibilities  of  the  case.  The  members  should 
have  marked  lines  of  division,  and  not  run  into  one 
another.  All  the  members  may  not  be  true ;  neither 
may  all  be  false. 


Article  V.     Other  Styles  of  Argument. 
Enthymeme  —  Sorites  —  Polysyllogism  —  Epichirem  —  Dilemma. 

108.  Argument  Abbreviated.  We  said  (No.  81)  that 
when  we  write  and  speak  we  do  not  always,  nor  even 
usually,  carry  on  an  ar«^umentation  with  completed 
syllogisms.  We  abbreviate.  The  various  methods  of 
abbreviation  give  us  various  styles  of  argument,  which 
have,  respectively,  their  proper  names. 

109.  Enthymeme.  If  we  drop  one  premiss  in  the  syllo- 
gism, the  argument  is  called  an  eiitlmmmc.     Example  : 


Therefore, 


All  liquids  will  flow  ; 
This  tar  will  flow. 


We  have  dropped  one  evident  premiss,  t/iis  tar  is  liquid, 
to  avoid  being  tiresome. 

Enthymeme  originally  meant  a  probable  argument; 
but,  by  a  mistake  as  to  its  derivation,  it  came  to  be 
applied  to  the  argument  where  one  premiss  is  kept  in 
the  mind.     In  this  sense  alone  is  the  word  now  used. 

110.  Sorites.  {Piled-up  argument.^  When  we  put 
down  three  or  more  premisses  and,  then,  one  conclusion 
following  from  them,  the  argument  is  called  a  Sorites. 
It  abbreviates  by  dropping  intermediate  conclusions.  It 
presumes  the  evidence  of  the  conclusion  after  the  first 
two  premisses,  and  adds  a  third  premiss  as  a  minor  to 


reasoning,  argument. 


65 


the  second  premiss  considered  as  a  major  ;  then  a  fourth 
premiss  as  a  minor  to  the  third  premiss  considered  as  a 
major,  etc.     Thus : 

He  who  tlespouds  ceases  to  labor; 

He  who  ceases  to  labor  makes  no  progress  ; 

He  who  makes  no  progress  does  not  reach  the  end. 

Therefore, 

He  who  desponds  does  not  reach  the  end. 

It  is  easy  to  see  that  this  is  an  abbreviation  of  two 
syllogisms.     Thus : 

He  who  desponds  ceases  to  labor; 

He  who  ceases  to  labor  makes  no  progress. 

Therefore, 

He  who  des2yonds  makes  no  progress. 

The  next  syllogism  begins  with  this  conclusion  as  a 
major : 

He  who  desponds  makes  no  progress ; 

He  who  makes  no  progress  does  not  reach  the  end. 

Therefore, 

He  tvho  desjyonds  does  not  reach  the  end. 

As  the  Sorites  involves  so  much  argument,  and  pro- 
ceeds so  rapidly,  we  must  be  cautious  with  an  adversary 
who  uses  it.  The  Sorites  may  be  drawn  out  to  any 
length.  Each  implied  syllogism  must  observe  the  laws 
of  the  syllogism. 

111.  PolysyUogism.  If  we  argue  with  a  chain  argu- 
ment, as  in  the  Sorites,  but  in  such  a  way  that  we  bring 
out  the  intermediate  conclusions,  not  explicitly  tiuiee  as 
above,  but  otice,  to  be  used,  simultaneously,  as  conclusion 


66 


THE    LAWS    OF    THOUGHT. 


to  the  two  preceding  premisses,  and  as  major  to  a  follow- 
ing minor,  our  argument  is  called  a  Polysyllogisin.  The 
preceding  example,  as  a  polysyllogism,  will  be  : 

He  ivho  dettpotuls  ceases  to  labor; 

He  ir/io  ceases  to  lahor  ftiahes  no  progress. 

Therefore, 

He  trfto  tfesj)ONt/s  niahes  tio  progress; 

He  irho  makes  no  progress  does  not  reach  the  end. 

Therefore, 

He  irho  desponds  does  not  reach  the  end, 

112.  Epichirem.  If  a  premiss,  or  even  each  j^remiss, 
requires  proof,  and  the  proof  is  attached  to  it  immedi- 
ately, whether  in  substance  or  in  full,  the  argument  is 
called  an  F.picliircm  {takifig  in  hand  the  doubted  premiss 
at  once).     I^lxample : 

One  irJto  (fenies  the  existence  of  Ciod  find  a  future 
life  cannot  ffc  trusted  in  societg ;  Incanse  he  ad- 
mits no  mot  ice  to  restrain  him  from  erif  when 
he  can  do  the  eril  irithont  temporal  inconren- 
ience. 

But  the  atheist  denies  the  existence  of  God  and  a 
future  life. 

Therefore, 

He  cannot  he  trusted  in  society, 

113.  Dilemma.  The  Dilemma  is  a  double  argument 
in  the  compass  of  a  single  syllogism.  It  may  be  even 
triple,  quadruple,  etc.  The  major  is  a  disjunctive  prop- 
osition. The  minor  takes  up  each  member  of  the  dis- 
junction, separately,  and  an  equally  satisfactory  conclu- 


REASONING,   ARGUMENT. 


6; 


sion  is  drawn  from  whichever  member  is  chosen.     Thus 
a  schoolboy  might  argue,  to  escape  his  evening  study : 

To-morrow  morning  it  will  be  either  raining  or  not 
raining, 

Jf  it  be  raining n  I  will  hare  an  excuse  to  stag  at 
hotne,  Jf  it  be  not  raining,  I  can  use  my  per- 
mission to  take  a  day  at  the  fair. 

Therefore, 

Jfliatercr  the  weather  may  be,  T  sJtall  not  hare  to 
go  to  school;  and  hence  I  need  not  study  my 
lessons  to-night. 

The    Dilemma   is   sometimes   a  very   useful   form   of 
argument  for  a  summary  refutation  of  false  theories. 


TRUTH    OF    THE    PREMISSES. 


69 


CIIAPTKR   V.     TRUTH    OF   THK    PRKMISSKS. 


Article  I.      Formal  and  Material  Logic. 

114.  The  Form.  Wc  have  seen  what  is  required  in  the 
quality  and  quantity  of  the  j)remisses,  and  in  the  exten- 
sion of  middle  and  extremes,  in  order  that  a  given 
conclusion  may  be  taken  as  lawfully  drawn  from  given 
premisses.     If  I  say, 

Kvery  steaiuhoat  is  a  fitnif1otret% 
Tlrefij  suN/fotrer  is  a  viofia. 
Therefore,  Erery  sfcatuhoftf  is  a  viotin^ 

and  suppose  the  premisses  to  be  true,  I  have  to  accept 
the  conclusion,  inevitably,  from  the  premisses.  The 
conclusion  is  in  perfect  accord  with  all  the  laws  of  the 
syllogism.  All  that  formal  logic  has  shown  us  to  be 
necessary  in  quality,  quantity  and  extension  has  been 
—  supposing  the  premisses  true  —  strictly  attended  to. 
Yet  every  proposition  in  the  strange  argument  is  false. 
This  leads  us  to  speak  of  the  matter  of  the  premisses, 
as  affecting  the  acceptance  of  the  conclusion.  We  shall 
say  something,  therefore,  on  the  truth  of  the  premisses. 
It  may  be  urged  that  the  subject  does  not  belong  strictly 
to  the /(?;7;/r?/ logic.  The  formal  logic  has  to  deal,  strictly 
speaking,  only  with  the  form,  or  structure,  of  argument 
necessary  to  have  a  conclusion  rightly  drawn  from  pre- 
misses;—  the  matter,  or  truth,  of  the  premisses  being 

68 


11 


left  out  of  consideration.     And  for  this  reason  is  it  called 
formal  logic.     By  this  is  it  distinguished  from  material 
logic. 

115.  The  Matter.  Material  logic  will  teach  us  what 
care  must  be  taken  in  the  use  of  the  various  means  we 
have  of  arriving  at  the  truth,  that  is  in  the  use  of  our 
various  faculties ;  and  when  we  may  cease  examining, 
and  rest  reasonably  secure  in  mind  as  to  the  truth  or 
falsity  of  what  is  expressed  in  a  proposition.  So  that,  if 
we  should  meet  with  a  syllogism  such  as  the  following. 

Every  timepiece  is  made  of  brass, 
All  brass  is  oryanie  matter, 
Therefore,  Kvery  timepiece  is  made  of  oryanie  matter, 

material  logic  would  have  to  tell  us  how  to  use  our 
faculties,  —  that  is,  how  far  to  trust  the  various  faculties 
—  in  our  search  for  truth  in  the  propositions.  It  is  only 
when  we  have  decided  as  to  how  far  we  are  to  admit 
the  propositions  that  the  work  of  formal  logic  begins. 
Nevertheless,  we  begin  the  study  of  philosophy  with 
formal  logic,  because  we  have  had  so  much  practical 
experience  in  the  use  of  our  faculties,  that  we  already 
hold  securely  that  many  propositions  are  true,  many 
others  false,  and  many,  again,  doubtful ;  and  we  want, 
at  once,  a  safe  and  systematic  rule  for  arguing  from  the 
known  to  the  unknown.  Therefore  we  study  formal 
logic  first. 

However,  we  shall  here  make  a  short  consideration 
upon  the  truth  and  falsity  of  the  premisses,  and  upon 
the  corresponding  adhesion  of  mind  which  we  can  give 
to  the  conclusion.  Yet  we  shall  do  this  in  such  a  way 
as  not  to  touch  the  question  of  the  means  we  have  for 
arriving  at  the  truth. 


ii 


70 


THE    LAWS    OF    THOUGHT. 


116.  Value  of  the  Conclusion.  We  cannot  hold  to  the 
conclusion  any  more  firmly  than  we  hold  to  the  prem- 
isses. Supposing  the  form  of  the  syllogism  to  be  correct, 
if  we  are  certain  of  the  truth  of  the  major  and  minor, 
we  may  be  certain  of  the  conclusion.  If  we  have  a 
lingering  doubt  as  to  the  truth  of  either  major  or  minor, 
that  doubt  will  cling  to  the  conclusion.  If  either  major  or 
minor  be  false,  the  conclusion  is  false;  and  the  argument 
is  called  a  sophism  or  a  fallacy.  Sophism  or  fallacy  is 
in  the  matter,  not  in  the  form.  A  defect  in  the  form  is 
called  a  paraUnrism.  This  has  been  abundantly  treated 
in  the  preceding  chapter  (Nos.  80-102). 

When  the  major  and  minor  are  both  truths  of  which 
we  are  certain,  the  argument  is  called  a  demonstration. 

Leaving  aside  the  ])robable  argument,  we  shall  treat 
of  the  demonstration  and  of  fallacies. 


Article    II.     The  Demonstr.\tion. 
Direct  —  Indirect  —  Simple  —  Compound  —  A  Priori  —  A  Posteriori. 

117.  Two  Kinds.  A  demonstration  is  an  argument  in 
which  the  conclusion  is  drawn  from  premisses  of  whose 
truth  we  are  certain.  It  may  be  direct  or  indirect ;  and 
either  kind  may  be  a  priori  or  a  posteriori. 

118.  Direct.  In  the  direct  demonstration  we  draw  the 
conclusion  we  desire,  directly  from  the  premisses  where 
we  have  compared  its  subject  and  its  predicate  with  a 
middle  term.     Thus : 


Therefore, 


The  HouJ  can  thinh-; 
Miittvr  rtniHof  think. 
The  soul  is  not  matter. 


1 1 


I 


truth  of  the  premisses. 


71 


119.  Indirect.  In  the  indirect  demonstration,  instead 
of  drawing  our  conclusion  as  coming  directly  from 
premisses  in  a  syllogism,  we  show  that  the  contradictory 
cannot  be  true,  by  exhibiting  the  absurd  consequences 
that  would  follow  from  such  contradictory.  The  indi- 
rect demonstration  is  of  frequent  use  in  geometry, 
where  we  show  absurd  consequences  that  would  follow 
from  not  admitting  the  theorem  laid  down. 

120.  Simple;  Compound.  A  demonstration  is  called 
simple  when  the  whole  argumentation  is  finished  clearly 
and  satisfactorily  with  a  single  syllogism.  If,  however, 
it  be  necessary  to  bring  forward  new  syllogisms  to  prove 
the  major  or  minor  or  both  —  which  may  not  be  clear, 
or  may  be  called  in  question  —  and,  perhaps,  again,  new 
sollogisms  to  prove  the  new  majors  or  minors,  the 
demonstration  is  called  componnd.  All  the  longer  theo- 
rems in  geometry  are  illustrations  in  point. 

121.  A  Priori.  An  argument  is  called  a  priori  when 
it  advances  from  premisses  which  state  truths  that  are 
prior  in  the  nature  of  things  to  the  truth  stated  in  the 
conclusion.  Thus  we  may  advance  from  what  we  know 
about  the  nature  of  a  cause  or  agent,  to  establish  some 
conclusion  regarding  the  nature  of  the  effect  it  may 
produce.  The  name  a  priori  is  used,  also,  for  an  argu- 
ment where  we  advance  from  principles  in  their  wider 
extension  to  an  application  of  the  same  principles  in  a 
less  wide  extension;  as,  for  instance,  from  principles 
regarding  the  whole  animal  kingdom  to  conclusions 
respecting  elephants  and  kangaroos.  Likewise,  when- 
ever we  advance  from  principles  to  facts,  as  from  the 
general  truths  about  triangles  to  the  exhibition  of  the 
truths  applied  in  a  particular  given  triangle. 


72 


THE    LAWS    OF    THOUGHT. 


122.  A  Posteriori.  The  a  posteriori  demonstration 
proceeds  in  the  opposite  direction.  It  advances  from 
what  is  posterior  in  the  nature  of  thinp^s  to  what  \s  prior 
in  the  nature  of  things.  From  the  existence  of  an  effect 
it  concUides  to  the  existence  of  a  cause ;  from  the  nature 
of  an  effect  to  the  nature  of  the  cause.  It  rises  from  a 
given  fact  to  the  principle  that  must  explain  the  fact. 
We  have  an  illustrious  example  of  the  a  posteriori  argu- 
ment in  the  discovery  of  the  planet  Neptune.  After  a 
quarter  of  a  century  of  observations  made  upon  the 
planet  Uranus,  discovered  by  Sir  W.  Herschel,  it  was 
found  that  its  movement  did  not  correspond  with  the 
known  forces  of  gravity  acting  upon  it,  especially  from 
Jupiter  and  Saturn.  There  was  a  fact:  movement. 
The  movement  must  have  a  cause.  The  cause  must 
be  a  heavenly  body.  The  movement  was  of  such  a 
character,  said  Leverrier,  that  if  it  came  from  a  single 
heavenly  body,  that  body,  at  a  given  time  would  be 
found  in  a  given  point  of  the  heavens.  The  telescope 
is  directed,  at  the  given  time,  to  the  given  point ;  and 
there  is  found  the  planet  Neptune  ! 


Article  III.     Induction. 
Complete  and  Incomplete  Induction  —  Example  —  Analogy. 

123.  Deduction  and  Induction.  We  add  here  a  special 
article  about  a  peculiar  kind  of  a  posteriori  argument, 
which,  by  custom,  has  been  allowed  to  appropriate,  as 
it  were,  the  name  Indnetton.  Every  a  posteriori  argu- 
ment is,  indeed,  an  iuduetioUy  as  opposed  to  the  a  priori 
argument,  which  is  a  deduction.     Deduction  means  the 


!i 


TRUTH    OF    THE    PREMISSES. 


73 


\'v- 


n 


ii 


drawing  out  of  a  particular  proposition  or  conclusion 
from  the  universal  premiss.  Induction,  on  the  contrary, 
is  a  leading  back  to  the  universal  from  the  particular. 
Every  process  of  thought  from  the  particular  to  the 
universal  is  inductive.  We  wish  to  speak  of  induction, 
in  the  usual  and  limited  acceptation  of  the  word,  as 
signifying  an  argument  which  passes  from  a  uniform 
experience  of  several  individual  cases  to  a  universal 
conclusion  covering  them  all.  The  induction  may  be, 
as  it  is  termed,  complete  or  incomplete. 

124.  Complete  Induction.  The  induction  is  called 
complete  when  after  having  really  made  an  examination 
of  all  the  cases  of  which  there  is  question,  and  having 
found  that  the  same  proposition,  varying  only  the  sub- 
ject, is  applicable  to  each  case  individually,  we  draw  a 
conclusion  in  which  we  include  them  all  in  a  single 
universal  proposition.  If,  for  instance,  I,  an  American, 
step  into  a  railway  car  and  finding  there  five  men.  A, 
B,  C,  D,  E,  I  discover  gradually  that  A  is  an  Ameri- 
can, that  B  is  an  American,  that  each  of  the  five  is 
an  American,  and  conclude  that  all  the  men  in  the 
car  are  Americans,  I  go  through  the  process  of  a 
complete  induction.  The  complete  induction  is  the 
exact  reverse  of  a  detailed  deduction,  in  which,  from  the 
universal,  that  all  the  men  in  the  car  are  Americans,  I 
would  conclude  :  A  is  an  American,  B  is,  C  is,  D  is,  E 
is,  I  am  an  American. 

We  may  sometimes  think  we  have  a  complete  induc- 
tion when,  in  reality,  we  have  not.  We  are  liable  to 
overlook  particular  cases.  Moreover,  sometimes  even 
when  the  greatest  care  is  taken  in  the  observation  of 
facts  in  certain  branches  of  the  natural  sciences,  when 


I 


74 


THE    LAWS    OF    THOUGHT. 


all  the  known  facts  have  been  classified  under  a  general 
proposition,  some  new  discovery  will  show  that  the 
general  proposition  is  untrue,  and  that  the  induction  was 
not  as  complete  as  it  was  believed  to  be. 

125.  Incomplete  Induction.  It  is  to  the  incomplete  in- 
duction, which  bears  the  name  in  the  strictest  sense,  that 
we  wish  to  call  particular  attention.  It  is  a  process  by 
which,  from  experience  of  a  limited  number  of  cases, we 
pass  on  to  formulate  a  universal  law.  Thus  we  formu- 
late the  laws  of  gravitation,  of  equilibrium,  of  reflection, 
of  refraction,  from  a  very  limited  number  of  cases ;  and 
we  hold  these  laws  to  be  applicable,  as  universal  proj)o- 
sitions,  to  cases  tried  and  untried.  Is  the  process  law- 
ful .? 

We  inquire  more  particularly  into  the  matter  because 
some  modern  logicians,  of  the  school  of  exj)erimentalists, 
make  the  study  of  induction  the  chief  business  of  logic. 
The  process  of  thought  may  be  accepted  as  lawful,  —  the 
experiments  having  been  rightly  conducted,  — but,  upon 
one    condition.      The    condition    is,  that  we  admit  the 
reality  of  such  a  thing  as  cause.     This  very  condition, 
which  is  absolutely  necessary  to  the  validity  of  the  process 
of  induction,  is  not  accepted  by  the  great  champion  of 
induction  among  the  experimentalists,  Mr.  J.  Stuart  Mill. 
The  process,  then,  is  lawful  if  we  admit  true  causality; 
namely,  that  whatever  begins  to  be,  depends  for  its  exist- 
ence upon  some  real  influence  exercised  by  something 
else  in  bringing  it  about.     In  other  words,  Every  effect 
demands  a  cause. 

Recognizing  this,  we  may  set  to  work  with  experiment 
and  observation  at  the  process  of  induction.  If  we  find, 
by  repeated  test,  that  the  same  consequent  follows  the 


TRUTH    OF   THE    PREMISSES. 


75 


same  antecedent  constantly  and  uniformly  in  whatsoever 
circumstances  or  adjuncts  of  time,  place,  quality  or  rela- 
tion the  antecedent  may  be  tried,  and  in  all  the  variations 
of  circumstances  by  composition,  opposition,  etc. ;  if  we 
find,  on  the  other  hand,  that,  suppressing  the  one  ante- 
cedent in  question,  whilst  leaving  all  the  circumstances 
and  adjuncts  the  same,  the  said  consequent  does  not 
make  its  appearance  in  any  of  the  cases  when  the  ante- 
cedent is  so  suppressed  ;  if,  again,  varying  the  antece- 
dent, in  the  various  cases,  in  quantity,  intensity,  direction, 
etc.,  we  find  that  the  consequent  varies  proportionally  in 
quantity,  intensity,  direction,  etc.  ;  in  other  words,  if  we 
find  that  said  consequent  follows  said  antecedent  only, 
but  always,  and  in  regular  proportion,  —  we  are  bound  to 
recognize  as  really  existing  in  said  antecedent  a  certain 
power  whereby  it  brings  into  existence  the  said  conse- 
quent ;  and,  also,  in  said  consequent,  a  certain  real 
dependence  for  its  existence  upon  the  antecedent.  We 
perceive  the  two  to  be  related  as  cause  and  effect.  But 
yet  more.  We  perceive  that  the  antecedent  is  cau.se  by 
rea.son  of  something  inherent  to  its  very  nature ;  for  we 
have  made  our  observations,  tests,  experiments,  abstract- 
ing from  it  everything  but  its  essential,  inherent  nature. 
But  the  essential,  inherent  nature  of  that  thing  must  be 
present  always  where  that  thing  is  ;  the  same  yesterday, 
to-day,  to-morrow.  Hence  we  conclude  that  the  same 
thing  will  produce  the  same  effect  to-morrow  as  to-day. 
We  formulate  a  universal  law  which  reaches  to  the 
future.  Mr.  J.  Stuart  Mill  has,  of  all  writers,  written 
best  upon  the  manner  of  making  the  tests  for  an  induc- 
tion. But  as  he  does  not  recognize  the  reality  of  cause, 
as  he  puts  no  real  connection  hoXwi^tw  foregoing  "diXi^  fol- 
lowing, his  conclusion  is  universal  only  to  the  extent  of 


y6 


THE    LAWS    OF    THOUGHT. 


the  tests  actually  made.     What  he  builds  up  with  one 
hand  he  tears  down  with  the  other. 

126.  Example.  Allied  to  induction  is  what  is  some- 
times called  the  argument  from  example.  It  concludes 
to  the  universal  from  a  few  cases ;  and,  even,  it  may  be, 
from  a  single  case,  without  the  tests  and  observations 
prescribed  for  induction.  Its  value  is  rather  in  discovery 
than  in  proof.  A  suj)erior,  well  trained  and  vigilant 
mind  will  often  suspect,  and  even  detect,  the  universal 
law  in  a  single  case ;  but  it  will  be  necessary  to  go 
through  the  various  tests,  to  make  the  law  acceptable  to 
the  ordinary  intelligence.  In  general  use  it  is  an  argu- 
ment weak  in  point  of  logic.  Logically,  it  sui^<:;csts  at 
most  the  possibility  of  a  case.  It  is  resorted  to  in  ora- 
torical discussion.  The  orator  has  the  advantajre  of 
forcing  his  listeners  on  without  giving  them  time  to 
examine,  and  urges  them  to  act  under  the  impression  of 
a  possibility. 

127.  Analogy.  The  argument  from  analogy  is  still 
less  reliable,  logically,  than  the  argument  from  example. 
It  is  a  pure  figure  of  rhetoric,  a  parallel  between  two 
cases  of  quite  different  orders.  It  is  useful  to  persuade 
an  audience  that  cannot  listen  to  dry  argument,  but  can 
listen  very  well  to  a  story,  and  then  follow  out  the  a])pli- 
cation  of  the  story,  in  all  its  details,  to  the  question 
under  treatment. 

128.  Caution.  In  philosophical  argument  be  wary  in 
the  use  of  example  and  analogy.  It  is  so  easy  to  giv^e 
illustrations  and  to  make  comparisons.  Therefore  have 
we  so  many  self-styled  "  scientists,"  to-day,  setting  them- 
selv^es  up  as  professional  discoverers,  and  flying  to  con- 
clusions which  the  slow,  careful  processes  of  induction 
do  not  warrant. 


TRUTH    OF    THE    PREMISSES. 


Article  IV.     Fallacies. 


17 


Begging  the  Question  —Evading  the  Question  —  Accident  —  A  Dicto 
Simpliciter,  etc.  —  Consequent  —  Cause  —  Question  —  Reference  — 
Objections. 

129.  Fallacy.  We  have  distinguished  the  Fallacy  or 
Sophism  from  the  Paralogism.  The  paralogism  is  an 
argument  with  a  flaw  in  the  form.  A  conclusion,  true 
in  itself,  may  be  found  in  a  syllogism  which  is  faulty  in 
the  form.  The  conclusion  may  be  true,  indeed,  but  it 
has  not  been  proved.  We  have  previously  considered 
arguments,  with  regard  to  the  correctness  of  the  form 
(Laws  of  the  Syllogism).  This  article  has  reference  to 
the  matter  of  the  conclusion.  Any  argument  with  a 
false  conclusion  is  a  fallacy.  The  word,  however,  is 
applied,  in  its  special  sense,  to  falsely  concluding  argu- 
ments which  have  so  much  the  appearance  of  correct- 
ness as  easily  to  deceive  the  unwary  or  to  silence  those 
whose  limited  knowledge  or  intelligence  does  not  enable 
them  to  detect  the  deceit.  We  shall  not  consider  any 
fallacy  which  is  an  evident  violation  of  the  laws  of  the 
syllogism.  Every  equivocation  is  such,  since  it  uses  a 
word  in  two  senses,  and  thus  gives  us  four  terms  in  the 
syllogism.  We  subjoin  some  fallacies  arising  from  the 
matter. 

130.  Petitio  Principii  or  Begging  the  Question.  This  is 
to  insert  cleverly  and  covertly  into  the  premisses  the 
very  thing  that  has  to  be  proved.  This  is  a  favorite 
fallacy  of  demagogues  haranguing  listeners  whose  hearts 
are  already  in  the  conclusion.  Communistic  gatherings 
echo  with  arguments  like  this : 


7« 


THE    LAWS    OF   THOUGHT. 


TRUTH    OF   THE    PREMISSES. 


79 


**A11  men  are  born  into  the  world,  equal,  with  equal 
rights  to  live,  equally,  upon  the  earth  and  to  enjoy  an 
equal  share  of  the  spontaneous  productions  of  the  earth. 
So  that  by  Nature  herself  are  they  justified  in  asserting 
their  equality  against  all  comers. 

**  Ikit  all  the  existing  laws  of  society  are  in  open  con- 
flict with  the  equal  rights  of  men  and  are  framed  only 
to  increase  the  inequality. 

**  Therefore,  as  we  cannot  get  the  rights  of  our  equal- 
ity from  society,  we  are  by  Nature  herself  justified  in 
overturning  governments  and  helping  ourselves." 

Here,  you  see,  the  right  to  plunder  is  assumed  covertly 
in  order  to  justify  plunder. 

The  circulus  vitiosus  {ricions  circle)  is  of  the  same 
order  as  Xhcpctitio principii.  We  prove,  for  instance,  the 
fall  of  the  apple  from  the  tree  by  gravitation  ;  and,  later 
on,  we  establish  gravitation  by  the  fall  of  the  apple. 

131.  Evading  the  auestion  {iirnorantia  clcnchi).  Under 
this  head  may  be  ranged  all  those  tricks  of  argument  by 
which  one  tries  to  make  the  best  of  his  case  without 
offering  proof;  or  to  shirk  an  objection  without  showing 
it  to  be  invalid.  This  may  be  done  by  assuming  for 
proof  or  disproof  something  similar  or  analogous  to  the 
point  in  question ;  or  by  attacking  an  opponent  on  the 
ground  that  he  is  not  to  be  regarded  as  an  authority  on 
the  subject  {arorHmcntitm  ad  Jiomincin),  thus  arousing 
prejudice  against  his  argument;  or  by  appealing  to  the 
passions  of  the  reader  or  listener ;  or  by  trying  to  shame 
an  opponent  out  of  the  debate  by  citing  against  him 
authorities  that  have  the  respect  of  the  listeners. 

This  is  an  utterly  illogical  way  of  proceeding,  but  it 
may  be  followed  with  great  effect. 


132.  Fallacy  of  the  Accident.  This  consists  in  assum- 
ing as  essential  what  is  purely  accidental.  Thus  a  man 
might  argue  against  Christianity  because  some  who  pro- 
fess it  are  not  exemplary  in  their  conduct.  However, 
evil-doers  are  never  such  by  reason  of  Christianity;  they 
may  be,  in  spite  of  it. 

133.  A  Dicto  Simpliciter  ad  Dictum  Secundum  Quid,  and 
vice  versa.  This  is  the  fallacy  of  arguing  from  aft  nn- 
qualified  stateuient  to  the  same  statement  qualified^  or  vice 
versa.  This  fallacy  pervades  daily  conversation.  From 
the  unqualified  statement  that  a  man  is  learned  the 
l)opular  mind  jumps  to  the  conclusion  that  he  is  learned 
in  particular  matters  to  which,  perhaps,  he  has  never 
given  any  attention.  How  many  a  man  truly  "learned" 
has  had  to  pay  for  his  name  as  "learned"  by  being 
consulted  as  though  he  were  an  encyclopaedia  .!*  This 
fallacy  works  with  equal  success  in  the  opposite  direc- 
tion. An  exhibition  of  some  knowledge  in  a  few  partic- 
ular matters  is  soon  made  the  basis  for  the  conclusion 
that  the  exhibitor  is  "learned." 

134.  Fallacy  of  the  Consequent.  This  consists  in  a 
misuse  of  the  conditional  syllogism.  Thus  some  one 
says :  If  the  gale  is  strong  to-night,  the  tourer  will  fall. 
In  the  morning  the  tower  is  found  to  have  fallen.  The 
fallacy  infers  that  the  gale  was  strong.  The  truth  is 
that  the  tower  may  have  fallen  under  other  agencies. 

135.  Fallacy  of  the  Cause.  This  lies  in  assuming  as  the 
cause  of  something  that  which  is  merely  an  accompany- 
ing or  preceding  circumstance,  or  at  most  an  occasion. 
Thus  we  sometimes  read  in  the  newspapers  that  the 
political  principles  of  a  party  in  power  are  the  cause  of 
all  the  fluctuations  in  trade.     Therefore,  to  secure  steady 


8o 


THE    LAWS    OF    THOUGHT. 


business,  the  administration  must  be  changed.  And 
when  the  administration  is  changed,  and  the  same  diffi- 
culties occur,  the  responsibility  is  shifted  to  the  oi)posite 
principles  of  the  new  party  in  power.  Or  we  read  that 
the  cause  of  a  bank  robbery  was  the  insecure  system  of 
bolts  put  on  by  a  certain  safe  company,  thus  shifting  the 
responsibility  from  the  want  of  vigilance  on  the  part  of 
the  authorities,  and  from  that  education  of  the  head 
without  the  education  of  the  heart,  so  prolific  in  evil- 
doers. 

136.  Fallacy  of  the  Question.  This  consists  in  asking 
a  number  of  questions  all  of  which  are  evidently  to  be 
answered  in  the  same  way,  by  yes  or  no ;  and  then  very 
deftly  inserting  one  question  whose  answer  should  be 
the  opposite,  but  which  is  made  to  pass  along  with  the 
others,  as  answerable  in  the  same  way.  Thus  the  com- 
munistic orator:  **  Are  we  poltroons.^  Shall  we  reject 
the  equality  nature  has  bestowed  upon  us  .^  Shall  we 
see  the  products  of  the  earth,  which  nature  intended  for 
all,  piled  up  for  the  use  of  a  few }  Can  we,  as  nature's 
freemen,  refuse  to  vindicate  our  equality.?  Is  there 
anything  to  prevent  us  from  destroying }  They  refuse 
us  a  share  in  their  millions.  Shall  we  refuse  them  a 
share  in  our  poverty.?  etc.     Therefore,  etc." 

137.  Fallacy  of  Reference.  This  is  untruth  —  the 
inventing  of  false  references  for  the  support  of  a  propo- 
sition. People  do  not  usually  verify  references,  and 
hence  may  be  easily  deceived  by  a  long  array  of  author- 
ities [.?]  cited  at  the  foot  of  the  page. 

138.  Fallacy  of  Objections.  This  consists  in  pouring 
forth   a   volume  of   objections,  one    immediately    after 


TRUTH    OF    THE    PREMISSES. 


8l 


another  before  giving  opportunity  for  reply.  The  adver- 
sary's time  may  be  more  than  taken  up  in  trying  to 
answer  one  of  them.  Even  then  his  long,  careful  answer 
may  not  be  as  effective  with  the  audience  (or  reader)  as 
the  terse,  captious  objection;  and  besides,  the  other 
objections  will  be  carried  away  unanswered. 


CHAPTER   VI.      MKTHOD. 


Articlp:  I.     Scientific  Method. 

139.  Scientific  Method.  Supposing  the  premisses  to  be 
true  and  the  form  of  correct  argumentation  to  be  fully 
understood  and  rigorously  applied,  there  are  still  differ- 
ent methods  which  may  be  followed  in  the  search  for 
conclusions,  in  the  pursuit  of  truth.  Moreover,  methods 
which  may  have  proved  most  satisfactory  to  our  own 
minds  in  the  search  for,  and  discovery  of  truth,  we  may 
find  less  satisfactory  for  conmnmicating  the  same  truth 
fully,  briefly,  and  clearly  to  others. 

We  do  not  refer  here  to  the  mere  variations  of  order 
m  which  a  number  of  truths,  such  as  dates  of  events  in 
history,  may  be  learned  or  communicated,  one  after 
another.  But  we  refer  to  methods  of  arriving  at  the 
knowledge  of  even  one  truth  as  a  conc/nswn,  U.  in  such 
a  way  as  to  possess,  together  with  the  truth,  also  the 
reasons  for  it.  We  speak  of  scientific  methods  which 
give  us  scientific  knowledge.  Science. 

140.  Analysis  and  Synthesis.  There  are  two  kinds  of 
scientific  method,  the  analytic  and  the  synthetic.  The 
analytic  proceeds  by  way  of  analysis  or  taking  apart  • 
the  synthetic,  by  way  of  synthesis  or  putting  together 
To  take  a  broad  example :  the  chemist  analyzes,  when 
he  proceeds  to  find  out  the  nature  and  proportions  of  the 
82 


METHOD. 


83 


various  elements  in  a  lump  of  crude  matter  brought  him 
from  the  mines ;  he  synthetizes,  when  he  puts  together 
various  chemical  elements  for  the  purpose  of  discovering 
some  new  law  of  combinations.  Thus  analysis  proceeds 
from  the  whole  to  the  parts  ;  synthesis,  from  the  parts 
to  the  whole. 

Before  considering  the  methods  of  synthesis  and 
analysis  we  shall  touch  upon  two  other  points, — defini- 
tion and  division,  —  the  understanding  of  which  will 
enable  us  to  speak  more  briefly  and  more  clearly  about 
the  methods. 


Article  II.     Definition. 

Nominal  —  Real  —  Descriptive  —  Genetic  —  Essential  —  Physical  — 

Metaphysical  —  Rules. 

141.  Definition.  Correct  definition  is  a  thing  always 
to  be  prized  in  writing  and  discourse,  even  for  its  effec- 
tiveness in  concentrating  vague  thought  and  shortening 
discussion.  A  universal  habit  of  correct  definition  would 
be  fatal  to  false  argument  and  would  put  an  end  to 
much  debate  that  is  carried  on  to  tiresome  lengths.  But 
the  habit  of  correct  definition  belongs  to  the  trained 
master  mind.  And  as  most  minds  are  not  such,  and 
as  most  men  shirk  the  search  and  labor  demanded  by 
correct  definition,  therefore  have  we  so  much,  in  phi- 
losophy as  in  other  things,  that  is  written  all  around  a 
subject  instead  of  about  it.  But  here  we  are  called  upon 
to  give  a  definition  of  a  definition.  Therefore  :  A  defini- 
tion is  the  expression  in  words  of  the  meaning  attached  to 
a  term  ;  or,  a  definition  is  the  expression  in  words  of  the 
nature  of  an  object.     That  is  to  say,  there  are  two  kinds 


84 


THE  LAWS  OF  THOUGHT. 


METHOD. 


85 


of  definition.  If  we  fix  our  attention  on  the  zvofdy  to 
make  it  known  in  its  character  as  a  si<^n,  we  have  the 
nominal  definition.  If  we  fix  our  attention  on  the  things 
to  define  what  /'/  is,  we  have  the  real  definition. 

142.  Nominal  Definition.  We  give  a  nominal  definition, 
(i)  When  we  make  known  the  sense  in  which  we  are 
using  a  term  for  the  case  in  question  ;  (2)  When  we 
make  known  the  meaning  usually  and  generally  given 
to  a  term  ;  (3)  When  we  declare  the  true  literal  mean- 
ing of  a  term  according  to  its  derivation.  Thus,  infinite^ 
from  the  Latin  ///  (a  negative  particle)  and  finis  (a 
limit),  means  without  limit. 

143.  Keal  Definition.  This  may  also  be  threefold, — 
descriptive,  genetic,  essential. 

The  descriptive  definition  is  nothing  more  than  a 
description.  It  does  not  enter  into  the  essence  of  the 
object.  It  gives  such  a  combination  of  accidental  fea- 
tures, circumstances,  etc.,  as  may  suffice  to  make  the 
object  recognizable.  Its  treatment  belongs  to  works  on 
composition  and  style. 

The  genetic  definition  (from  genesis,  origin)  gives  the 
process  by  which  a  thing  is  produced.  A  genetic 
definition  of  a  circle  would  be:  A  plane  surface  gene- 
rated by  revolving  a  straight  line  about  one  of  its  extremi- 
ties fixed. 

The  essential  definition  names  the  essential  parts  of 
an  object ;  that  is,  those  without  which  the  object  can 
neither  be  nor  be  thought  of.  According  to  the  way 
in  which  we  look  at  an  object,  we  may  find  it  made  up 
of  separable  essential  parts  which,  taken  together,  will 
give  us  the  whole  essence ;  or  of  inseparable  essential 
parts  which,  considered  as  taken  together,  will  also  give 


i 


us  the  whole  essence.  Such  separable  parts  are  called 
{physical  parts,  and  the  enumeration  of  them  is  the 
real  essential  physical  definition.  Such  non-scparablc 
jiarts  are  called  metaphysical  parts,  and  the  enumeration 
of  them  is  the  real  essential  metaphysical  definition. 
Thus,  in  man,  spiritual  soul  and  organic  body  are  essen- 
tial parts ;  they  embrace  all  that  is  essential ;  they  are 
actually  separable;  taken  together,  they  give  us  the 
essence.  Hence  to  say  that  man  is  a  being  composed  of 
a  spiritual  soul  and  an  organic  body,  is  to  give  an  essen- 
tial physical  definition  of  man.  Again,  in  man,  animal 
nature  and  rational  nature  are  essential  parts;  they 
embrace  all  that  is  essential ;  taken  together,  they  give 
us  the  entire  essence.  But  they  are  not  physically,  that 
is  actually,  separable.  Take  away  rational  nature,  and 
you  have  not  animal  nature  left,  but  only  a  dead  body  ; 
for  the  principle  of  life  is  gone.  Such  parts  are  sepa- 
rable only  in  the  consideration  of  the  mind ;  that  is,  in  an 
order  of  things  outside  the  real  physical  order,  — or,  in 
the  metaphysical  order.  They  are  called  metaphysical 
j)arts.  Hence  to  say  that  man  is  a  rational  animal,  is 
to  give  the  essential  metaphysical  definition  of  man. 
This  is  the  true  definition  in  logic.  It  classifies  accord- 
ing to  those  logical  considerations  spoken  of  in  Chapter 
II.,  Article  II.  It  gives  the  species  by  combining  the 
two  essentials  of  proximate  genus  and  final  difference ; 
and  there  is  no  mistaking  a  thing  thus  defined.  —  It  is 
the  perfect  definition. 

144.  Rules  for  Definition.  We  may  summarize  the 
requisites  of  a  good  definition : 

I.  The  terms  of  the  definition  should  convey  a  more 
definite  idea  than  the  single  term  expressing  the  thing 


u 


86 


ixlE    LAWS    OF    THOUGHT. 


defined.  This  does  not  mean  that  every  term  in  the 
definition  should  always  be  at  once  better  known  by 
everybody  than  the  single  term.  When  we  define  a 
circle  to  be  a  plane  surface  with  a  sifigle  curved  line  for 
a  boundary  every  point  ofwhic/i  is  ec/ually  distant  from  one 
fixed  point  in  the  surface,  our  definition  is  less  intelli- 
gible to  an  ignorant  person  than  is  the  term  circle.  But 
one  who  learns  the  meaning  of  the  terms  in  the  defini- 
tion will  get  from  it  a  more  definite  idea  than  he  had 
before  possessing  the  definition  of  a  circle. 

2.  Make  the  definition  such  that  it  may  be  convert- 
ible by  simple  conversion  (No.  76)  with  the  term  express- 
ing the  object  defined.  Thus :  if  a  circle  is  a  plane 
surface  .  .  .  etc.,  then  a  plane  surface  .  .  .  etc.  {as  above) 
is  a  circle. 

3.  Do  not  define  by  a  negation,  by  saying  what  a 
thing  is  not.  However,  sometimes  a  negative  term 
comes  up  for  definition.  In  this  case  separate  it  into  its 
negative  and  positive  parts,  and  define  the  positive  part. 
For  instance,  injustice  is  the  absence  of  justice.  Now 
i\c^int  justice y  and  you  shall  have  defined  injustice. 

4.  Use  words  in  their  exact  literal  meaning;  and 
when  there  is  a  choice  of  words,  use  such  as  are  most 
commonly  understood. 

5.  In  philosophical  matters  insist  upon  the  essential 
metaphysical  definition.  It  may  sometimes  be  useful 
to  begin  with  or  to  work  upon  the  physical  definition; 
but  never  lose  sight  of  the  metaphysical. 


METHOD. 


87 


Article  III.     Division. 

145.  Scientific  Division.  Definition,  the  perfect  logical 
definition,  regards  the  comprehension  of  a  term  (Chapter 
III.,  Article  V.).  Division,  the  perfect  logical  division, 
regards  the  extension.  This  difference  we  must  exam- 
ine into  as  being  of  serious  importance  in  all  scientific 
study.  A  few  words,  however,  first,  upon  division  in 
general  and  on  certain  divisions  which  are  precisely 
the  inverse  of  the  essential  definition  whether  physical 
or  metaphysical. 

146.  Parts,  Physical  and  Metaphysical.      We  saw  that 
essential  definition  (No.  143)  is  the  enumeration  of  the 
essential  parts,  as  taken  together  to   form  the  whole. 
Division,  in  general,  is  a  separation  of  whatever  may  be 
regarded  as  a  whole,  a  unit,  into  its  parts.     If  we  regard 
an  essence  as  a  whole,  a  unit,  made  up  of  the  parts 
enumerated  in  the  essential  physical  definition,  we  have 
what  is  called  a  physical  whole,  which  is  divisible  by 
physical,  actual  division  into  physical  parts.     Thus  man, 
considered  as  a  physical  whole,  is  divisible  actually  into 
the  physical  parts,  spiritual  soul  and  organic  body.     If, 
however,  we  regard  an  essence  as  a  whole,  a  unit,  made 
up  of  the  parts  enumerated  in  the  essential  metaphysical 
definition,  we  have  what  is  called  a  metaphysical  whole, 
which  is  divisible  by  metaphysical,  mental  division  into 
metaphysical  parts.     Thus  man,  considered  as  a  meta- 
physical whole,  is  divisible  into  the  metaphysical  parts, 
animal  nature  and  rational  nature. 

147.  Actual  Union.  The  union  of  parts  in  both  cases 
is  an  actual  union.  The  physical  parts,  however,  are 
really  separable ;  the  metaphysical  parts,  only  mentally. 


S8 


THE  LAWS  OF  THOUGHT. 


METHOD. 


89 


148.  Integral  Parts.  Parts  which  arc  really  separable 
but  which  are  not  essential,  t'.c  not  absolutely  necessary 
for  the  existence  of  the  whole,  though  belonging  to  its 
integrity  or  entirety,  are  called  integral  parts.  A  hand 
or  a  foot  is  an  integral  part  of  man. 

To  summarize,  therefore:  A  whole,  regarded  in  its 
essence  as  made  up  of  real  parts  actually  existing,  may 
be  considered  as  made  up  of  physical  parts,  really  sepa- 
rable ;  or  of  metaphysical  parts  not  really  separable. 

Physical  parts  which,  though  belonging  to  the  normal 
state  of  the  whole,  to  its  integrity,  yet  can  be  separated 
without  destroying  the  essence,  are  called  integral. 
Thus :  a  hand  or  a  foot  in  man. 

149.    Logical  Division.     To  return  now  to  logical  divis- 
ion :  the  parts  we  are  especially  concerned  with,  in^this 
article,  and  which  we  are  to  get  at  by  logical  division, 
are  not  such  as  are  bound  together  in  actual  union  by 
an  actual  bond  of   unity,  so  as  to  make  a  real,  actual 
something.      We  are  concerned   with  another  kind  of 
parts,  those,  namely,  which  are  embraced  by,  and  go  to 
make  up  the  extension  of  an  idea  or  term,  not  those 
which  are  found  in  comprehension.     We  said  that  the 
perfect  definition  was  the  enumeration  of  notions  con- 
tained in  the  comprehension.     The  perfect  division  is 
the  enumeration  of,  the  partitioning  off  of  what  can  be 
reached  by  the  extension  of  a  term.     This  logical  divis- 
ion  is  therefore   the  enumeration,  the  dividing  up,  of 
species   under  genus,  or  of    individuals   under  species. 
A  genus  is  a  logical  whole;   the  .species  under  it  and 
their    subdivisions   are    logical    parts.     A   species    is    a 
logical  whole ;  the  individuals  it  extends  to  are  logical 
parts. 


The  following  diagram  will  explain  better  than  words 
the  precise  distinction  between  logical  definition  and 
logical   division.      To  define  animal,  we  go  upwards, 


Substance 
Material 
Organic 

A 

Sentient 


PeW"^ 


ANIMAL  = 


Rational  (Man). 


Irrational. 


[CV«»rfks,  Frederic,  Augustus,  Hannibal,  Scipio,  etc.|  |  Vertcbrat.a,  Arliculata,  Mollusc.-*,  Radial*  | 


r 


ir 


I 


t:iking  in  the  various  notions  in  the  comprehension  : 
sentient,  organic,  material,  substance.  To  divide  animal, 
we  go  downwards,  classifying  all  that  can  be  reached  by 
the  extension  of  the  term. 

150.  Potential  Parts.  Every  term  taken  in  the  reflex 
universal  sense  (Nos.  21,  23)  expresses  a  whole  which  is 
divisible  by  this  kind  of  division  into  the  parts  of  its 
extension.  As  thus  divisible  it  is  called  a  potential 
whole,  because  it  extends  not  only  to  what  really  exists, 
but  also  to  what  exists  only  in  potentia;  that  is,  to  what- 
ever of  the  same  kind  may  exist.  All  the  birds  in  the 
universe  might  be  destroyed,  still  bird  would  express  a 
potential  whole  embracing  all  birds  past  and  all  birds 
possible  in  the  present  and  the  future  though  they  shall 
not  all  exist,  —  embracing  them  all  as  potential  parts 


It- 


90 


THE    LAWS    OF    THOUGHT. 


into  which  it  {bird)  is  capable  of  being  divided  by  logi- 
cal division. 

151.  Logical  Whole.  This  kind  of  whole,  then,  is  the 
logical  whole  ;  becftuse,  being  the  object  of  a  reflex  uni- 
versal idea,  it  does  not  exist  as  a  unit  in  reality,  but 
only  by  consideraticm  of  the  mind.  Thus  vuui,  consid- 
ered as  the  object  (Nos.  21,  23)  of  the  reflex  universal 
idea,  is  not  a  one  something  that  can  actually  be  torn 
asunder  into  separate  men;  nor  can  substance,  taken  as 
the  object  of  a  reflex  universal  idea,  be  really  split  up 
into  material  and  immaterial  substance.  Yet  in  the 
mysterious  process  of  thought,  niati,  substance^  do  logi- 
cally embrace  all  men,  all  substances,  actual  and 
possible. 

152.  Importance  of  Division.  It  is  the  logical  division 
which  we  must  be  careful  to  have  special  regard  for,  in 
philosophizing.  Philosophy  deals  with  the  universal. 
It  is  from  beginning  to  end  a  combination  and  correla- 
tion of  the  comprehension  and  extension  of  ideas.  The 
advantage  of  correct  logical  division  in  the  study  of  a 
subject  is  evident.  It  maps  out  the  whole  question 
before  us,  at  the  start ;  and  saves  us  from  time-losing, 
wandering  discussions,  as  well  as  from  incomplete  treat- 
ment of  the  matter  in  hand. 

153.  How  to  Divide.     To  divide  correctly  : 

1.  Let  the  sum  of  the  parts  be  exactly  equal  to  the 
whole. 

2.  Therefore  see  that  no  single  member  of  the  divis- 
ion is  equal  to  the  whole.  A  bad  division  of  plants 
would  be  into  those  that  grow  and  those  that  bear  fruit. 
The  first  member  is  equal  to  the  whole. 


1 


METHOD. 


91 


3.  Do  not  make  one  member  to  include  another  or 
part  of  another.  This  would  happen  if  substance  were 
divided  into  immaterial^  material^  living  and  organic. 
Living  enters  into  material  and  immaterial.  Organic 
enters  into  living  and  material. 

4.  Divide  first  into  proximate  and  immediate  mem- 
bers, and  then,  if  possible,  subdivide.  The  meaning  of 
this  is  that  we  should  first  seek  the  widest  general 
grand  divisions  and  then  see  if  we  cannot  regard  these 
as  new  wholes  to  be  subdivided,  etc. 

5.  In  scientific  matters  prefer  the  logical  division. 
See  if  the  whole  may  not  be  regarded  as  a  genus. 
Mark  off  the  species.  See,  again,  if  any  species,  thus 
found,  may  be  regarded,  in  its  turn,  as  a  genus  (Chapter 
II.,  Article  III.) ;  and  do  not  go  on  to  divide  into  indi- 
viduals until  a  species  cannot  be  regarded  as  a  new 
genus.     (See  Diagram  No.  30). 


Article  IV.     Analysis  and  Synthesis. 

154.  The  Question  Put.  We  may  now  go  on  to  the 
explanation  of  the  methods  referred  to  above  (Nos.  139, 
140).  A  proposition  is  presented  to  us  in  study,  reflec- 
tion, reading,  conversation,  debate.  Is  it  true  or  false } 
We  make  an  assertion.  We  do  not  doubt  the  truth  of 
our  proposition,  but  how  shall  we  proceed  to  place  it  in 
evidence,  by  means  of  demonstration }  An  adversary 
advances  a  false  statement.  How  shall  we  prove  it  to 
be  false  .'*  A  single  object  of  thought  is  offered  us  for 
investigation.  What  propositions  shall  we  formulate 
regarding  it  ?  What  shall  we  predicate  of  it }  Of  what 
may  it  be  predicated } 


92 


THE  LAWS  OF  THOUGHT. 


METHOD. 


93 


155.  The  Answer :  Analysis  and  Synthesis.  Our  inves- 
tigation of  any  single  object  of  thought  must  begin  by 
analysis  or  synthesis,  and  must  advance  by  one  or  the 
other,  either  purely  by  analysis  or  purely  by  synthesis, 
or  by  changing  about,  as  circumstances  may  prompt, 
from  one  to  the  other.  Let  the  object  of  thought  pre- 
sented for  investigation  be  animal.  We  must  begin  by 
trying  to  make  animal  the  subject  or  the  predicate  of  a 
proposition.  If  we  begin  by  making  it  a  subject,  we  are 
using  analysis  ;  we  are  beginning  by  the  analytic  method. 
If  we  begin  by  trying  to  use  it  as  a  predicate,  we  are 
using  synthesis;  we  are  beginning  by  the  synthetic 
method.  Again,  an  entire  proposition  is  presented  to 
us  :  Animal  is  substance,  or  Animal  is  not  mineral.  We 
have  to  test  the  truth  of  the  proposition.  We  must 
begin  by  studying  the  subject  or  the  predicate.  If  we 
begin  with  the  subject,  we  are  using  analysis;  if  with 
the  predicate,  we  are  using  synthesis.  The  meaning  of 
all  this  and  the  reasons  for  the  terminology  will  best  be 
seen  in  the  case  of  a  complete  proposition. 

156.  Analysis.  Take  the  propositions.  Animal  is  sub- 
stance. Animal  is  not  mineral.  Are  they  true.?  We 
know  that  in  an  affirmative  proposition  the  form  (No. 
20)  of  the  predicate  is  included  in  the  comprehension  of 
the  subject  (No.  66)  ;  and  that  in  the  negative  propo- 
sition the  form  of  the  predicate  is  excluded  from  the 
comprehension  of  the  subject  (No.  ^%).  Suppose  we 
begin  by  a  study  of  the  subject.  To  see  whether  the 
forms,  substance,  mineral,  are  comprehended  in  animal, 
we  must  take  animal  apart  into  all  the  forms  implied  in 
its  comprehension.  We  must  analyze  it.  We  do  this 
by  taking  it  as  a  metaphysical  zvhole,  proceeding  upward 


(No.  149)  from  the  metaphysical  whole,  ^;//;;W,  through 
all  the  forms,  parts,  of  its  comprehension.  There  we 
find  substance  embraced  in  the  comprehension,  but  not 
mineral.  Hence  animal  is  substance,  animal  is  not 
mineral.  The  process  is  nothing  more  than  logical 
definition. 

157.  Synthesis.  On  the  contrary,  if  we  begin  by  the 
study  of  the  predicate,  since  we  know  that  in  an  affir- 
mative proposition  the  predicate  expresses  some  form 
that  is  contained  in  the  comprehension  of  the  subject, 
we  shall  —  if  the  predicate  be  not  merely  the  essential 
definition  of  the  subject  (No.  66)  — we  shall  have  to 
keep  adding  on  to  it  what  is  compatible  with  it  until  we 
shall  have  gathered  together  all  the  forms  embraced  in 
the  comprehension  of  the  subject.  Thus  (No.  149)  we 
keep  on  adding  material,  organic,  sentient,  one  after 
another,  to  substance,  until  we  get  a  combination  that 
gives  us  animal.  This  is  synthesis.  The  process  is  that 
of  logical  division.  In  the  case  of  a  negative  proposi- 
tion,—if  it  be  true,  — we  may  keep  on  adding  to  the 
predicate  forever,  and  we  shall  never  find  a  combination 
giving  us  the  subject.  This  proves  that  the  negative 
proposition  is  true.  If  in  an  affirmative  proposition 
we  fail  to  find  the  subject,  this  shows  the  proposition  to 
be  false. 

158.  The  Explanation  Complete.  These  few  words 
cover  all  the  essentials  of  synthesis  and  analysis  as  sci- 
entific methods.  The  words  analysis  and  synthesis  are 
sometimes  used  in  ways  that  are  apt  to  confuse  the 
mind.  Reduce  every  mode  of  expression  back  to  that 
of  comprehension,  remembering  that  it  varies  inversely 
with  extension,  and  the  confusion  will  disappear. 


94 


THE    LAWS    OF   THOUGHT. 


I 


159.  Singular  to  Universal,  and  Vice  Versa.  It  is  said 
that  analysis  proceeds  from  the  singular,  or  particular,  or 
less  universal,  to  the  more  universal ;  and  that  synthesis 
proceeds  from  the  more  universal  to  the  less  universal. 
This  would  seem  to  contradict  all  that  we  have  been 
saying.  But  remember  that  reference  is  here  made 
to  the  extension,  which  varies  inversely  with  the  com- 
prehension. When  we  proceed  from  animal  up  to 
snbstancc,  we  go  from  the  less  universal  to  the  more 
universal  /;/  extension,  though  from  the  wider  to  the  less 
wide  comprehension.  Hence  there  is  analysis  in  both 
cases. 

160.  Complex  to  Simple,  and  Vice  Versa.  It  is  said  that 
analysis  goes  from  the  complex  to  the  simple  ;  synthesis, 
from  the  simple  to  the  complex.  Understand  this  of 
comprehension.  This  manner  of  expression  is  applied  to 
the  process  from  particular  concrete  facts  to  the  universal 
law,  for  analysis;  and  to  the  process  from  the  law  to 
particular  applications,  for  synthesis.  But  how  is  the 
single  fact  complex  and  the  universal  law  simple.^  You 
will  see  it  in  an  illustration.  You  argue  from  the  par- 
ticular concrete  facts  regarding  matter,  to  a  universal 
law  regarding  matter.  The  single  fact  is  complex.  The 
matter  you  have  is  this  or  that  kind  of  matter,  organic, 
inorganic,  vegetable,  animal,  mineral,  gaseous,  liquid, 
etc.  You  have  a  complex  comprehension.  You  have 
to  analyze  the  separate  cases,  and  cut  away  from  the 
comprehension,  until  you  arrive  at  the  simpler  form, 
matter,  simpler  in  comprehension,  more  universal  in 
extension,  to  make  your  general  law  about  all  matter, 
without  specifying  this  or  that  particular  kind  of  matter. 

Induction  is  analytic.     Deduction  is  synthetic. 


METHOD. 


95 


161.  Discovery  and  Instruction.  The  modern  growing 
natural  sciences  grow  by  analysis.  The  sciences  that 
have  been  explored  to  satisfaction  and  present  a  com- 
plete whole,  as  also  growing  sciences,  —  botany,  chemis- 
try, etc.,  — so  far  as  they  have  been  explored  and  classified, 
are  best  tanght  by  the  synthetic  method.  Analysis 
is  best  for  discovery.  Synthesis  is,  in  general,  more 
satisfactory  for  instruction.  The  two  methods  may  be 
used  alternately,  in  the  same  treatment  of  the  same 
subject.  A  change  is  sometimes  useful  in  the  treatment 
to  rouse  attention. 

162.  Analytic  and  Synthetic  Sciences.  A  science  is 
called  analytic  or  synthetic  from  the  method  chiefly 
used  in  its  development.  If,  however,  both  methods 
enter  very  largely  on  account  of  the  nature  of  the 
subject-matter,  we  have  the  mixed  method,  properly  so 
called.  Logic  and  geometry  are  synthetic.  The  vari- 
ous branches  that  make  up  the  modern  physics  are 
analytic.  Civil  engineering,  taken  as  a  whole,  is  mixed ; 
it  implies  the  synthetic  mathematics  and  also  the  result 
of  analytic  observation  on  material  to  be  used,  as  well  as 
climatic  conditions,  etc.  —  In  this  little  book  we  have 
mingled  analysis  whenever  it  seemed  useful  for  clear- 
ness or  interest. 

163.  Advice.  With  what  has  been  said,  the  student 
will  be  enabled  to  follow  up  the  complete  working  of 
synthesis  and  analysis  by  attention  to  the  processes 
pursued  in  standard  treatises  on  the  various  sciences. 

If  you  find  yourself  confronted  with  the  burden  of 
proof  or  investigation,  observe  the  following : 

1.  Work  cautiously. 

2.  Consult  your  actual  knowledge.     The  general  out- 


< 


96 


THE    LAWS    OF    THOUGHT. 


METHOD. 


97 


line  of  your  actual  kno\viecl<;c  may  determine  your 
method.  Particulars  may  be  so  scanty  that  you  will  see 
your  way  to  lie  only  throu<;h  ^^eneral  principles,  by  syn- 
thesis. Or  facts  may  be  in  such  abundance  that  you 
may  set  to  work  at  once  by  analysis. 

3.  Ik'ware  of  being  unconsciously  betrayed  into  a 
fallacy. 

4.  He  on  the  alert  for  the  moment  when  you  can 
formulate  a  definition  of  terms. 

5.  In  distributing  and  classifying,  keep  in  view  the 
logical  division. 

6.  When  you  have  found  something  by  analysis,  go 
over  it  again  by  synthesis.  This  will  map  it  out  in  your 
memory. 


Article    V.     Scuince. 

164.  Science.  With  a  clear  understanding  of  what  is 
recjuired  for  correct  thought,  and  with  some  insight  into 
methods  of  procedure,  we  may  go  in  pursuit  of  knowd- 
cdge.  l^:very  perception  of  any  truth  is  knowledge.  If 
this  perception  be  through  a  demonstration,  it  is  called 
.scientific  knowledge.  The  perception,  through  demon- 
stration, of  a  complete  body  of  related  truths  regarding 
a  given  object,  is  called  science. 

165.  Object  of  a  Science.  The  same  object  may  be 
the  o/?/cr/  of  more  than  one  science.  For  we  may  con- 
sider the  same  object  under  different  aspects;  and 
obtain,  regarding  it,  different  sets-of-connected-truths  — 
each  set  complete  without  the  other.  In  other  words, 
we  may  consider  different  forms,  or  formalities,  found 
in  the  totality  of  the  comprehension  of  the  object. 


166.    Material  and  Formal  Object.     The  object,  taken 
in  the  totality  of  its  comprehension,  is  called  the  maU- 
rial  object  of  a  science.    The  particular  formality  consid- 
ered, or  this  formality  as  affecting  the  material  object  — 
abstraction  made  from  all  the  other  formalities  compre- 
hended—is called  \h<i  formal  object  of  the  science.    The 
whole  corporeal  universe  is  the  material  object  v.gr.  of 
both  astronomy  and  chemistry.     But  the  formal  object 
of   the  .science  of  astronomy  is  the  mass,  magnitude, 
distance,  co-ordinated  motions,  etc.,  of  the  various  masses 
of  matter,  called  heavenly  bodies,  which  make  up  the 
corporeal  universe ;  whilst  the  formal  object  of  chemis- 
try is  the  substantial  distinction  between  elements  of 
matter   and  their   respective    capacities   for   substantial 
union  with  one  another.     Again,  various  things,  even  of 
different   orders,  may  be    united    into   one   science    by 
reason  of  a  formality  running  through  them  all.     Thus, 
spirit,  matter,  substance,  accident,  all   contain   in   their 
comprehension,  the    formality    of    bciu^ ;    and    can    be 
taken  all  together  as  the  material  object  of  the  science 
of  being.     They  can    all   be   considered    in   the   same 
science,'\mder  the  aspect  of  being,  and  this  will  give  us 
the  science  of  Ontology. 

167.  A  Delusion.  Knowledge  acquired  by  scientific 
processes  is  scientific  knowledge.  The  possession  of 
such  knowledge  is  the  possession  of  science.  No  other 
knowledge  has  a  right  to  the  name.  Children  in  pri- 
mary schools  who  are  obliged  to  memorize  a  few  facts 
about  rocks  or  animals  or  flowers,  are  often  instructed 
to  a  false  acceptation  of  the  word  by  being  told  that 
they  are  '*  studying  science "  !  !  Thus  they  come  to 
regard  geology,  zoology,  botany,  any  and  every  science, 
as'^merely  a  list  of  facts,  and  the  acquisition  of  a  science 
to  be  an  affair  of  memory  and  not  of  reason. 


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98 


EXPLANATION    OF    OUTLINE. 


99 


In  the  preceding  table  or  "  Outline  of  the  Sciences  "  we  have  advanced  from 
the  term  of  least  comprehension  and  greatest  extension^  namely,  the  term,  Being. 
That  which  is  represented  by  the  term  or  concept  Being  supplies  the  subject- 
matter  for  Ontology,  the  Science  of  Being. 

We  go  on  trying  to  increase  the  comprehension  and  diminish  the  extension 
by  adding  the  terms,  Finite  and  Infinite,  to  Being.  The  division  is  not  one 
of  genus  into  species,  as  we  have  seen  when  speaking  of  analogy  (Nos.  28,  36), 
yet  it  serves  us  for  this  very  broad  outline.  Infinite  Being  is  the  subject-matter 
of  the  science  calleil,  in  philosophy,  Natural  Theology. 

Continuing  with  Finite  Being,  increasing  comprehension  and  diminishing  ex- 
tension, we  have,  in  a  perfect  division,  Sikstantial  Finite  Being  and  Acciden- 
tal Finite  Being.  Ontology  extends  thus  far,  defniing  the  notions  of  Infinite 
and  Finite,  and  treating  of  Substance  and  of  all  that  is  not  Substance,  that  is  of 
Accident;   quantity,  quality,  action,  time,  space,  etc.     It  is  general  i)hilosophy. 

Again  dividing,  and  increasing  comprehension,  we  have  Material  SlBSTAN- 
TiAL  Finite  Bein(;  and  SriKiTiAL  Sikstantial  Finite  Being.  We  do  not  treat 
of  bodiless  spirit  under  the  Finite,  in  philosophy,  liut  taking  the  Matekial,  in  the 
wide  sense  of  the  term,  we  have  the  subject-matter  of  the  science,  Cosmology. 

Increasing  the  comprehension,  again,  by  adding  Animate  and  Inanimaif,  we 
get  in  the  Animate  Material,  etc.,  the  subject-matter  of  the  science,  Biology,  as 
general  science  of  life.  If  we  take  the  other  subdivision.  Inanimate  Material, 
etc.,  we  find  that  range  of  sciences  which  treat  of  inanimate,  inorganic  matter : 
Physics,  etc. 

We  leave  the  INANIMATE;  and  we  divide  the  Animate,  by  adding  to  the  com- 
prehension, into  the  Rational  and  the  Irrational.  The  Irrational  divided  by 
adding  to  comprehension,  gives  us  Sensitive  and  Non-Sensitive  (the  brute 
and  the  plant),  with  the  sciences.  Sensation,  etc..  Vegetation,  etc. 

Returning  to  Rational  Animate,  etc.,  we  find  here  the  science  of  Man 
in  general,  or  Anthropology.  From  this  point  forward  we  are  engaged 
solely  with  Man.  We  can  no  longer  divide  into  species.  We  use  such  divisions 
as  will  give  us  a  complete  and  clear  view  of  the  subject,  Man. 

By  actual  physical  essential  division  (No.  146)  we  can  divide  Man  into 
Soul  and  Animal  Body.  The  Animal  Body,  for  general  princi]ilcs,  we  refer 
over  to  Sensation.  Soil  is  the  subject-matter  of  the  Science,  Psychology. 
Psychology  will  treat  of  the  Nature  of  the  Soul  and  the  Po^vers  of  the  Soul. 
The  Po7vers  of  the  Soul,  we  group  under  three  headings:  Power  of  actuating 
sense-perception,  tic. \    Intellect;   Pree-lVill. 

Intellect,  we  consider  in  its  Nature;  its  Method  of  Work;  its  Supply  of 
Material.  The  Method  of  Work  constitutes  the  object  (or  subject-matter)  of 
the  Science,  Formal  Logic.  The  Supply  of  Material  for  true  thought  gives 
us  the  object  of  the  Science,  Material  Logic 

Under  the  heading  of  Free  Will  we  treat  of  the  Existence  and  Nature  of  Free 
Will;  of  the  Norma  or  Rule  of  the  Free  Act;  and  oi  Practical  Morality.  7 he 
Existence  and  Nature  of  Free  Will,  we  may  readily  refer  to  the  treatise  on  the 
Po7vers  of  the  Soul.  In  this  way,  accepting  Free  Will  from  Psychology,  we  have, 
left,  the  Norma  of  P>ee  Act  and  Practical  Morality.  These  last  two,  Norma  and 
Practice,  taken  together,  form  the  subject-matter  of  the  Science,  Ethics. 

This  is  one  presentation  of  the  philosophical  and  subsidiary  sciences.  In  study- 
ing, we  begin  upon  the  lowest  line  with  Formal  Logic.  Next,  we  take  up  Material 
Logic.  Thus  equipped,  we  go  back  to  Ontology,  and  follow  do\\n  through  the 
Finite  until  we  reach  the  border  line  of  Ethics.  Here,  we  turn  back  to  take  up 
the  study  of  Natural  Theology,  which  we  had  omitted  and  for  which  we  are  now 
prepared.  At  length,  with  what  philosophy  can  teach  us  of  God  and  man  and  of 
the  wide  universe  about  us,  we  study,  in  Ethics,  the  practical  conclusions  to  be 
drawn  from  the  whole,  to  guide  the  actions  of  the  free,  inteUigent  being,  Man. 


POINTS  FOR  PRACTICE.  —  The  practical  utility  of  Formal 
Logic,  and  the  mental  training  to  be  derived  from  it,  depend  alto- 
gether upon  the  skill  acquired  in  readily  discerning  the  comprehen- 
sion and  extension  of  terms.  The  Laws  of  the  Syllogism  —  Detinition, 
Division,  Synthesis,  and  Analysis  —  are  all  to  be  learned  by  the  care- 
ful study  of  Extension  and  Comprehension.  Special  attention  should 
be  given  to  these  two  correlated  points.  Original  illustrations  should 
be  sought  for  as  a  proof  that  those  in  the  book  have  been  understood. 

(9)  Name  objects  (jf  the  simple  apprehension  or  of  the  idea.  (10)  (iive 
examples  of  judgments.  (ll)  Upon  what  two  principles  does  the  mind 
work  in  reasoning?  (13-15)  What  is  a  term,  a  proposition,  a  syllogism? 
(17-19)  (iive  three  classiiications  <jf  ideas.  (19)  Kxampks  of  singular, 
particular,  collective,  universal  ideas.  (20)  How  are  universal  ideas  classi- 
tied?  What  is  meant  l)y  form,  formality,  or  determination,  in  reference  to 
ideas?     (21-27)  Kxa!nj)lcs  of  species,  genus,  diflerence,  property,  accident. 

(29)  Name  some  forms  that  may   he  used  i^oth  as  generic  and  specihc. 

(30)  (iive  illustrations  of  hij^hest    genus,  lowest  species,  subaltern  j^enera. 
Tables  of  contents  in  scientific  works  will  furnish  examples.     (32)   Exam- 
ples of  real  and   loj^ical  terms.      (33-35)    Univocal  and  equivocal  terms. 
(36)   What  is  an  analogous  term  ?  and  why  is   the   question  of  analogy 
introduced  here?     (37)  Lxamples  of  the  material,  logical,  real  supposition 
of  terms.     (40)  Examples  of  proj)ositions,  pointing  out  the  sul)ject,  copula, 
and  predicate.     (41)  Kxamples  showing  the  difference  between  the  logical 
and  the  grammatical  predicate,      (42)   Kxamples  of  simj)le.      (43)  Com- 
pound.    (45,  46)  Categorical,  conditional.      (47,  48)  Conjunctive  and  dis- 
junctive prt)positions.     .Show  how   tlu'y  are   reducible  to  the  conditional. 
(54,  55)  Kxamples  of  a  priori  and  a  posteriori  judgments.     Show  why  the 
a  priori  are  called  necessary,  absolute,  metaphysical,  analytical;   antl  the 
f/ /tJi/t'r/t^/'/,  contingent,  hypothetical,  j>hysical,  synthetical.     (59-61)  What 
is  meant  by  the  extension  and  comprehension  of  terms  or  ideas?     (62-63) 
What  does  the  extension  of  a  proposition  depend  upon?     Examples  of  the 
fi>ur  extensions  of  propositions.      (65-70)    Kxplain  the  laws  which  declare 
the  extension  of  the  predicate    in  universal   and   particular  propositions, 
both  affirmative  and  negative.      Name  and  illustrate  the  one  exception  for 
tiie  universal  affirmative.      (73)    State  what   is  absolutely  necessary  that  a 
proposition  may  have  the  force    of  a   negation.      (76)    Kxamples  of  the 
conversion  of  propositions,  retaining   and  changing  (juantity  and  quality. 
(78)  Of  opposition  in  (juantity  and    ijuality.      (84)   Kxplain  the  difference 
between  conse<|uent    and   consecjuence.       (86)  Give    the    analysis   of  an 
(original)  argument.      (SS)   Kxplain    the  true,  primary  meaning  of  Middle 
Term.    (92)  What  is  meant  by  the  Moods  of  the  Syllogism?    (94-102)  Nine 
Laws  of  the  Syllogism.     Compose  faulty  arguments  or  syllogisms,  and  show 
how  each  law  may  be  violated.     (104-107)  Kxamples  of  syllogisms.    Show 
how   the    conjunctive    and    disjunctive    are    reduced    to    the    conditional. 
(108-II3)    Kxamples    of    enthymeme,    sorites,    polysyllogism,    epichirem, 
dilemma.       (i  14-122)     Difference    between    formal    and    material    logic; 
between   direct   and    indirect    demonstration;     between    simple   and   com- 
pound;   between   the   a  priori  and  the  a   posteriori.      (124)   Kxample  of 
complete  induction.     (125)  What  is  rocjuired  for  the  validity  of  the  incom- 
plete induction?      (i2()-f38)  Kxamples  of  various  fallacies.     (145)  What 
is  the  essential  distinction  between  logical  definition  and  logical  division? 
(146)  What  is  meant  by  physical  and  metaphysical  jiarts?    (149-153)  What 
is  a  logical  whole?  logical  ilivision?  What  are  logical  parts? 

100 


ALPHABETICAL    INDEX. 


Numbers  refer  to  Paragraphs. 


Abstract  idea,  17. 

Accident,  inseparable  and  separable, 
26,  27. 

fallacy  of,  132. 
Accidental  form,  27. 
Adequate  idea,  18. 
A  dicto  simpliciter,  fallacy,  133. 
Affirmative  proposition,  72. 
Analogy,  argument  from,  127. 
Analogous  terms,  33,  36. 
Analysis,  140,  155,  156. 

explanation  of  terminology  in  regard 
to,  159,  160. 

in  discovery  and  instruction,  161. 
Antecedent  in  syllogism,  83. 
Apprehension,  simple,  9. 

as  an  act,  9. 

as  representative,  9. 
A  prion  demonstration,  117,  121. 

judgment,  55. 
A  posteriori  iXcvcvQXisAxdXxow,  wj,  122. 

judgment,  56. 
Argument,  11,  15,  80. 

analysis  of,  86. 

basis  of,  II,  85. 

styles  of,  81. 
Argumentation,  11. 
Axioms,  for  extension  and   compre- 
hension of  terms,  58. 

for  argument,  11,  85. 

Begging  the  question,  130. 
Being,  predication  of,  28,  36. 
science  of,  166. 


Cause,  fallacy  of  the,  135. 
Caution,  103. 
Clear  idea,  18. 
Collective  idea,  19. 
Collective  proposition,  63. 
Complete  idea,  18. 
Compound  demonstration,  120. 
Comprehension     and     extension    ol 
terms,  axiom  regarding,  58. 

of  idea  and  term,  60,  61. 

in  analysis  and  synthesis,  156,  157. 
Comprehensive  idea,  18. 
Concept,  9. 
Conclusion,  11,  86. 

value  of,  116. 
Concrete  idea,  17. 
Consequence,  84. 
Consequent,  fallacy  of,  134. 

in  syllogism,  83. 
Conversion  of  propositions,  76. 


Declaration,  10. 

Deduction,  11,  123. 
Definition,  141. 

nominal,  142. 

real,  descriptive,  genetic,  essential, 
physical,  metaphysical,  143. 

logical,  143,  156. 

logical,  diagram  of,  149. 

logical  and  division,  difference  be- 
tween, 145. 

rules  for,  144. 
Delusion,  a,  167. 

lOI 


I02 


ALPHABETICAL     INDEX. 


Demonstration,  ii6. 

direct,  117,  118. 

indirect,  117,  119. 

simple  and  compound,  120. 

a  priori  and  a  posteriori,  117,  121, 
122. 
Determination  or  form,  20. 
Diagram  of  figures  in  syllogism,  89, 
90,  91. 

of  genus,  species,  etc.,  30. 

of  logical  definition  and  division,  149. 

of  propositions,  79. 

of  sciences,  168. 

of  seventh  law  for  syllogism,  100. 
Difference,  specific,  25. 
Differential  idea,  25. 
Dilemma,  81,  113. 
Direct  demonstration,  117,  118. 

universal  idea,  21. 
Discovery  by  analysis  and  synthesis, 

161. 
Distinct  idea,  18. 
Division,  145. 

physical,  metaphysical,  mental,  146. 

logical,  150,  151,  156. 

logical,  diagram  of,  149. 

importance  of,  152. 

rules  for,  153. 

Elenchi,  ignorantia,  131. 
Enthynienie,  81,  109. 
Epichirem,  81,  112. 
Equipollence  of  propositions,  77. 
Equivalence  of  propositions,  'j'j. 
Equivocal  terms,  33,  35. 
Example,  argument  from,  126. 
Extension  of  terms  and  ideas,  59,  61. 

of  terms,  axiom,  58. 

of  predicate,  66,  71. 
Extremes,    extreme   major  term,   ex- 
treme minor  term,  87,  88. 
Evading  the  question,  131. 

Fallacies,  130-138. 

Fallacy,  116,  129. 

Figures  of  syllogism,  88-91. 


Form  (formality  or  determination), 
20. 

specific,  22. 

generic,  24. 

accidental,  27. 

when  f)oth  generic  and  specific,  29. 
Formal  logic,  2,  114,  115. 

Genera,  subaltern,  31. 
Generic,  24. 

idea,  24. 

and  specific,  the  same  form,  29. 
Genus,  24. 

highest,  31. 
Grammatical   predicate,  logical   and, 
41. 

Herschel,  Sir  W.,  122. 
Highest  genus,  31. 

Idea,  9. 

characteristics  of,  18. 

classifications  of  ideas,  17-19. 

comprehension  of,  60,  61. 

differential,  25. 

extension  of,  59,  61. 

generic,  24. 

object  of  universal  reflex,  23. 

specific,  22. 
Ii^norautia   elenchi,  131. 
Indirect  demonstration,  117,  119. 
Induction,  123. 

complete,  124. 

incomplete,  125. 
Inference,  11. 

Judgment,  10,  38. 

as  an  act,  10. 

as  representative,  10. 

immediate,  51. 

mediate,  52. 

a  priori,  necessary,  absolute,  meta- 
physical, analytical,  55. 

a  posteriori,  contingent,  hypotheti- 
cal, physical,  synthetical,  56. 

synthetic  a  priori,  57. 


ALPHABETICAL    INDEX. 


103 


Kant,  57. 

Knowledge,  representative,  8. 

Laws  of  extension  of  predicate,  71. 

of  syllogism,  93-102. 
Leverrier,  122. 
Logic,  artificial,  4. 

as  an  art,  6. 

as  a  science,  5. 

formal,  2,  114,  115. 

material,  2,  114,  115. 

natural,  3. 

the  name,  i. 
Logical   and  grammatical  predicate, 
41. 

supposition  of  terms,  37. 
Lowest  specieS,  31. 

Major  extreme,  87,  88. 

premiss,  83,  88. 
Material  logic,  2,  114,  1 15. 
Material  supposition  of  terms,  37. 
Method,  advice  regarding,  163. 

analytic,  154-162. 

mixed,  162. 

scientific,  139. 

synthetic,  154-162. 
Mill,  J.  Stuart,  125. 
Mind,  three  acts  of,  7. 
Minor  extreme,  87,  88. 

premiss,  83,  88. 
Moods  of  syllogism,  92. 

Negative  particle,  73. 

proposition,  72. 
Notion,  9. 

Object  of  a  science,  165,  166. 

material,  166. 

formal,  166. 
Objections,  fallacy  of,  138. 
Objective,  identity,  10. 
Ontology,  166. 

Opposition  of  propositions,  78. 
Oral  expression  of  thought,  12. 


Paralogism,  116. 
Particular  idea,  19. 

proposition,  63. 
Parts,  physical,  metaphysical,  separa- 
ble,  inseparable,   integral,  unioa 
of,  146-148. 

potential,  150. 
Petitio  principii,  130. 
Polysyllogism,  81,  iii. 
Predicables,  heads  of,  28. 
Predicate  of  a  proposition,  40,  65. 

logical  and  grammatical,  41. 

laws  of  extension,  66-71. 
Premisses  in  syllogism,  83. 

major,  83. 

minor,  83. 
Principii  petitio,  130. 
Property,  26. 
Proposition,  14,  39. 

simple,   complex,   42;    compound, 

43- 
possible  varieties  of,  44. 

categorical,  45. 

conditional  or  hypothetical,  46. 

conjunctive,  47. 

disjunctive,  48. 

extension    of,    singular,   particular, 

collective,  universal,  62.  63. 
use  of  name  "  particular,"  64. 
extension  of  predicate  in,  66-71. 
affirmative,  negative,  72. 
quality  and  quantity  of,  74. 
relations  of,  conversion,  equivalence 

or  equipollence,  opposition,  75-78. 

Question,  begging  the,  130. 
fallacy  of  the,  136. 

Real  supposition  of  terms,  37. 
Reasoning,  11,  80. 

as  an  act,    as  representative,  two 
working  principles,  11. 

process  of,  53. 
Reference,  fallacy  of,  137. 
Reflex  universal  idea,  21. 

object  of,  23. 


I04 


ALPHABETICAL    INDEX. 


Science,  164. 

object  of  a,  165. 

material  and  formal  object,  166. 
Simple  apprehension,  9. 

demonstration,  120. 
Singular  idea,  19. 

proposition,  63. 
Sopliism,  116. 
Sorites,  81,  no. 
Species,  22,  23. 
Specific,  22. 

difference,  25. 

idea,  22. 

and  generic,  the  same  form,  29. 
Subaltern  genera,  31. 
Subject  of  a  proposition,  40. 
Supposition   of  terms,  real,  material, 

logical,  37. 
Syllogism,  15,  81,  82. 

antecedent,  major  and  minor  prem- 
iss, consequent  in,  83. 

consequence  in,  84. 

figures  of,  88-91. 

moods  of,  92. 

laws  of,  93-102. 

simple, compound,  conditional,  con- 
junctive, disjunctive,  104-107. 
Synthesis,  140,  155,  157. 


explanation  of  terminology   in   re- 
gard to.  159,  160. 
in  discovery  and  instruction,  161. 
Synthetic  a  priori  judgment,  57. 

Term,  13. 

classification  and  use,  32. 
univocal,  equivocal,  analogous,  33- 

36. 

comprehension  and  extension,  59- 
61. 

extreme,   extreme    major,   extreme 
minor,  middle,  87. 

supposition  of,  real,  material,  logi- 
cal, 37. 
Thought,  form  of,  2. 

material  of,  2. 

oral  expression  of,  12. 

Universal  idea,  19. 

idea,  direct,  21. 

idea,  reflex,  21. 

idea,  reflex,  object  of,  23. 

proposition,  63. 
Univocal  terms,  33,  34. 

Whole,  logical,  151. 
metaphysical,  146,  156. 
physical,  146. 


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